diff --git a/pkg/core/blockchain.go b/pkg/core/blockchain.go
index 982886bcc..45d124d85 100644
--- a/pkg/core/blockchain.go
+++ b/pkg/core/blockchain.go
@@ -1245,8 +1245,8 @@ func (bc *Blockchain) GetScriptHashesForVerifying(t *transaction.Transaction) ([
 }
 
 // GetTestVM returns a VM and a Store setup for a test run of some sort of code.
-func (bc *Blockchain) GetTestVM() *vm.VM {
-	systemInterop := bc.newInteropContext(trigger.Application, bc.dao, nil, nil)
+func (bc *Blockchain) GetTestVM(tx *transaction.Transaction) *vm.VM {
+	systemInterop := bc.newInteropContext(trigger.Application, bc.dao, nil, tx)
 	vm := SpawnVM(systemInterop)
 	vm.SetPriceGetter(getPrice)
 	return vm
diff --git a/pkg/core/blockchainer/blockchainer.go b/pkg/core/blockchainer/blockchainer.go
index 5b84826b4..2a9664246 100644
--- a/pkg/core/blockchainer/blockchainer.go
+++ b/pkg/core/blockchainer/blockchainer.go
@@ -41,7 +41,7 @@ type Blockchainer interface {
 	GetScriptHashesForVerifying(*transaction.Transaction) ([]util.Uint160, error)
 	GetStorageItem(scripthash util.Uint160, key []byte) *state.StorageItem
 	GetStorageItems(hash util.Uint160) (map[string]*state.StorageItem, error)
-	GetTestVM() *vm.VM
+	GetTestVM(tx *transaction.Transaction) *vm.VM
 	GetTransaction(util.Uint256) (*transaction.Transaction, uint32, error)
 	mempool.Feer // fee interface
 	PoolTx(*transaction.Transaction) error
diff --git a/pkg/network/helper_test.go b/pkg/network/helper_test.go
index fe60dac6d..70ad94bb8 100644
--- a/pkg/network/helper_test.go
+++ b/pkg/network/helper_test.go
@@ -97,7 +97,7 @@ func (chain testChain) GetScriptHashesForVerifying(*transaction.Transaction) ([]
 func (chain testChain) GetStorageItem(scripthash util.Uint160, key []byte) *state.StorageItem {
 	panic("TODO")
 }
-func (chain testChain) GetTestVM() *vm.VM {
+func (chain testChain) GetTestVM(tx *transaction.Transaction) *vm.VM {
 	panic("TODO")
 }
 func (chain testChain) GetStorageItems(hash util.Uint160) (map[string]*state.StorageItem, error) {
diff --git a/pkg/rpc/request/param.go b/pkg/rpc/request/param.go
index 3f5f9acfa..87af906fc 100644
--- a/pkg/rpc/request/param.go
+++ b/pkg/rpc/request/param.go
@@ -7,6 +7,7 @@ import (
 	"fmt"
 	"strconv"
 
+	"github.com/nspcc-dev/neo-go/pkg/core/transaction"
 	"github.com/nspcc-dev/neo-go/pkg/encoding/address"
 	"github.com/nspcc-dev/neo-go/pkg/smartcontract"
 	"github.com/nspcc-dev/neo-go/pkg/util"
@@ -65,6 +66,7 @@ const (
 	TxFilterT
 	NotificationFilterT
 	ExecutionFilterT
+	Cosigner
 )
 
 func (p Param) String() string {
@@ -154,6 +156,47 @@ func (p Param) GetBytesHex() ([]byte, error) {
 	return hex.DecodeString(s)
 }
 
+// GetCosigner returns transaction.Cosigner value of the parameter.
+func (p Param) GetCosigner() (transaction.Cosigner, error) {
+	c, ok := p.Value.(transaction.Cosigner)
+	if !ok {
+		return transaction.Cosigner{}, errors.New("not a cosigner")
+	}
+	return c, nil
+}
+
+// GetCosigners returns a slice of transaction.Cosigner with global scope from
+// array of Uint160 or array of serialized transaction.Cosigner stored in the
+// parameter.
+func (p Param) GetCosigners() ([]transaction.Cosigner, error) {
+	hashes, err := p.GetArray()
+	if err != nil {
+		return nil, err
+	}
+	cosigners := make([]transaction.Cosigner, len(hashes))
+	// try to extract hashes first
+	for i, h := range hashes {
+		var u util.Uint160
+		u, err = h.GetUint160FromHex()
+		if err != nil {
+			break
+		}
+		cosigners[i] = transaction.Cosigner{
+			Account: u,
+			Scopes:  transaction.Global,
+		}
+	}
+	if err != nil {
+		for i, h := range hashes {
+			cosigners[i], err = h.GetCosigner()
+			if err != nil {
+				return nil, err
+			}
+		}
+	}
+	return cosigners, nil
+}
+
 // UnmarshalJSON implements json.Unmarshaler interface.
 func (p *Param) UnmarshalJSON(data []byte) error {
 	var s string
@@ -167,6 +210,7 @@ func (p *Param) UnmarshalJSON(data []byte) error {
 		{TxFilterT, &TxFilter{}},
 		{NotificationFilterT, &NotificationFilter{}},
 		{ExecutionFilterT, &ExecutionFilter{}},
+		{Cosigner, &transaction.Cosigner{}},
 		{ArrayT, &[]Param{}},
 	}
 
@@ -196,6 +240,8 @@ func (p *Param) UnmarshalJSON(data []byte) error {
 				} else {
 					continue
 				}
+			case *transaction.Cosigner:
+				p.Value = *val
 			case *[]Param:
 				p.Value = *val
 			}
diff --git a/pkg/rpc/request/param_test.go b/pkg/rpc/request/param_test.go
index 032173446..e6ada2ced 100644
--- a/pkg/rpc/request/param_test.go
+++ b/pkg/rpc/request/param_test.go
@@ -5,6 +5,7 @@ import (
 	"encoding/json"
 	"testing"
 
+	"github.com/nspcc-dev/neo-go/pkg/core/transaction"
 	"github.com/nspcc-dev/neo-go/pkg/encoding/address"
 	"github.com/nspcc-dev/neo-go/pkg/smartcontract"
 	"github.com/nspcc-dev/neo-go/pkg/util"
@@ -19,9 +20,13 @@ func TestParam_UnmarshalJSON(t *testing.T) {
                  {"cosigner": "f84d6a337fbc3d3a201d41da99e86b479e7a2554"},
                  {"sender": "f84d6a337fbc3d3a201d41da99e86b479e7a2554", "cosigner": "f84d6a337fbc3d3a201d41da99e86b479e7a2554"},
                  {"contract": "f84d6a337fbc3d3a201d41da99e86b479e7a2554"},
-                 {"state": "HALT"}]`
+                 {"state": "HALT"},
+                 {"account": "0xcadb3dc2faa3ef14a13b619c9a43124755aa2569", "scopes": 0},
+                 [{"account": "0xcadb3dc2faa3ef14a13b619c9a43124755aa2569", "scopes": 0}]]`
 	contr, err := util.Uint160DecodeStringLE("f84d6a337fbc3d3a201d41da99e86b479e7a2554")
 	require.NoError(t, err)
+	accountHash, err := util.Uint160DecodeStringLE("cadb3dc2faa3ef14a13b619c9a43124755aa2569")
+	require.NoError(t, err)
 	expected := Params{
 		{
 			Type:  StringT,
@@ -83,6 +88,25 @@ func TestParam_UnmarshalJSON(t *testing.T) {
 			Type:  ExecutionFilterT,
 			Value: ExecutionFilter{State: "HALT"},
 		},
+		{
+			Type: Cosigner,
+			Value: transaction.Cosigner{
+				Account: accountHash,
+				Scopes:  transaction.Global,
+			},
+		},
+		{
+			Type: ArrayT,
+			Value: []Param{
+				{
+					Type: Cosigner,
+					Value: transaction.Cosigner{
+						Account: accountHash,
+						Scopes:  transaction.Global,
+					},
+				},
+			},
+		},
 	}
 
 	var ps Params
@@ -214,3 +238,67 @@ func TestParamGetBytesHex(t *testing.T) {
 	_, err = p.GetBytesHex()
 	require.NotNil(t, err)
 }
+
+func TestParamGetCosigner(t *testing.T) {
+	c := transaction.Cosigner{
+		Account: util.Uint160{1, 2, 3, 4},
+		Scopes:  transaction.Global,
+	}
+	p := Param{Type: Cosigner, Value: c}
+	actual, err := p.GetCosigner()
+	require.NoError(t, err)
+	require.Equal(t, c, actual)
+
+	p = Param{Type: Cosigner, Value: `{"account": "0xcadb3dc2faa3ef14a13b619c9a43124755aa2569", "scopes": 0}`}
+	_, err = p.GetCosigner()
+	require.Error(t, err)
+}
+
+func TestParamGetCosigners(t *testing.T) {
+	u1 := util.Uint160{1, 2, 3, 4}
+	u2 := util.Uint160{5, 6, 7, 8}
+	t.Run("from hashes", func(t *testing.T) {
+		p := Param{ArrayT, []Param{
+			{Type: StringT, Value: u1.StringLE()},
+			{Type: StringT, Value: u2.StringLE()},
+		}}
+		actual, err := p.GetCosigners()
+		require.NoError(t, err)
+		require.Equal(t, 2, len(actual))
+		require.True(t, u1.Equals(actual[0].Account))
+		require.True(t, u2.Equals(actual[1].Account))
+	})
+
+	t.Run("from cosigners", func(t *testing.T) {
+		c1 := transaction.Cosigner{
+			Account: u1,
+			Scopes:  transaction.Global,
+		}
+		c2 := transaction.Cosigner{
+			Account: u2,
+			Scopes:  transaction.CustomContracts,
+			AllowedContracts: []util.Uint160{
+				{1, 2, 3},
+				{4, 5, 6},
+			},
+		}
+		p := Param{ArrayT, []Param{
+			{Type: Cosigner, Value: c1},
+			{Type: Cosigner, Value: c2},
+		}}
+		actual, err := p.GetCosigners()
+		require.NoError(t, err)
+		require.Equal(t, 2, len(actual))
+		require.Equal(t, c1, actual[0])
+		require.Equal(t, c2, actual[1])
+	})
+
+	t.Run("bad format", func(t *testing.T) {
+		p := Param{ArrayT, []Param{
+			{Type: StringT, Value: u1.StringLE()},
+			{Type: StringT, Value: "bla"},
+		}}
+		_, err := p.GetCosigners()
+		require.Error(t, err)
+	})
+}
diff --git a/pkg/rpc/server/server.go b/pkg/rpc/server/server.go
index 1068c2a2d..5cbda8f88 100644
--- a/pkg/rpc/server/server.go
+++ b/pkg/rpc/server/server.go
@@ -618,7 +618,7 @@ func (s *Server) getDecimals(h util.Uint160, cache map[util.Uint160]int64) (int6
 	if err != nil {
 		return 0, response.NewInternalServerError("Can't create script", err)
 	}
-	res := s.runScriptInVM(script)
+	res := s.runScriptInVM(script, nil)
 	if res == nil || res.State != "HALT" || len(res.Stack) == 0 {
 		return 0, response.NewInternalServerError("execution error", errors.New("no result"))
 	}
@@ -864,11 +864,21 @@ func (s *Server) invokeFunction(reqParams request.Params) (interface{}, *respons
 	if err != nil {
 		return nil, response.ErrInvalidParams
 	}
-	script, err := request.CreateFunctionInvocationScript(scriptHash, reqParams[1:])
+	tx := &transaction.Transaction{}
+	checkWitnessHashesIndex := len(reqParams)
+	if checkWitnessHashesIndex > 3 {
+		cosigners, err := reqParams[3].GetCosigners()
+		if err != nil {
+			return nil, response.ErrInvalidParams
+		}
+		tx.Cosigners = cosigners
+		checkWitnessHashesIndex--
+	}
+	script, err := request.CreateFunctionInvocationScript(scriptHash, reqParams[1:checkWitnessHashesIndex])
 	if err != nil {
 		return nil, response.NewInternalServerError("can't create invocation script", err)
 	}
-	return s.runScriptInVM(script), nil
+	return s.runScriptInVM(script, tx), nil
 }
 
 // invokescript implements the `invokescript` RPC call.
@@ -882,13 +892,21 @@ func (s *Server) invokescript(reqParams request.Params) (interface{}, *response.
 		return nil, response.ErrInvalidParams
 	}
 
-	return s.runScriptInVM(script), nil
+	tx := &transaction.Transaction{}
+	if len(reqParams) > 1 {
+		cosigners, err := reqParams[1].GetCosigners()
+		if err != nil {
+			return nil, response.ErrInvalidParams
+		}
+		tx.Cosigners = cosigners
+	}
+	return s.runScriptInVM(script, tx), nil
 }
 
 // runScriptInVM runs given script in a new test VM and returns the invocation
 // result.
-func (s *Server) runScriptInVM(script []byte) *result.Invoke {
-	vm := s.chain.GetTestVM()
+func (s *Server) runScriptInVM(script []byte, tx *transaction.Transaction) *result.Invoke {
+	vm := s.chain.GetTestVM(tx)
 	vm.SetGasLimit(s.config.MaxGasInvoke)
 	vm.LoadScript(script)
 	_ = vm.Run()
diff --git a/pkg/rpc/server/server_test.go b/pkg/rpc/server/server_test.go
index 2560f786c..72e9a28fa 100644
--- a/pkg/rpc/server/server_test.go
+++ b/pkg/rpc/server/server_test.go
@@ -620,6 +620,55 @@ var rpcTestCases = map[string][]rpcTestCase{
 				assert.NotEqual(t, 0, res.GasConsumed)
 			},
 		},
+		{
+			name: "positive, good witness",
+			// script is hex-encoded `test_verify.avm` representation, hashes are hex-encoded LE bytes of hashes used in the contract with `0x` prefix
+			params: `["5707000c14010c030e05060c0d020e0f0d030e070900000000db307068115541f827ec8c21aa270700000011400c140d0f03020900020103070304050201000e060c09db307169115541f827ec8c21aa270700000012401340",["0x0000000009070e030d0f0e020d0c06050e030c01","0x090c060e00010205040307030102000902030f0d"]]`,
+			result: func(e *executor) interface{} { return &result.Invoke{} },
+			check: func(t *testing.T, e *executor, inv interface{}) {
+				res, ok := inv.(*result.Invoke)
+				require.True(t, ok)
+				assert.Equal(t, "HALT", res.State)
+				require.Equal(t, 1, len(res.Stack))
+				require.Equal(t, int64(3), res.Stack[0].Value)
+			},
+		},
+		{
+			name:   "positive, bad witness of second hash",
+			params: `["5707000c14010c030e05060c0d020e0f0d030e070900000000db307068115541f827ec8c21aa270700000011400c140d0f03020900020103070304050201000e060c09db307169115541f827ec8c21aa270700000012401340",["0x0000000009070e030d0f0e020d0c06050e030c01"]]`,
+			result: func(e *executor) interface{} { return &result.Invoke{} },
+			check: func(t *testing.T, e *executor, inv interface{}) {
+				res, ok := inv.(*result.Invoke)
+				require.True(t, ok)
+				assert.Equal(t, "HALT", res.State)
+				require.Equal(t, 1, len(res.Stack))
+				require.Equal(t, int64(2), res.Stack[0].Value)
+			},
+		},
+		{
+			name:   "positive, no good hashes",
+			params: `["5707000c14010c030e05060c0d020e0f0d030e070900000000db307068115541f827ec8c21aa270700000011400c140d0f03020900020103070304050201000e060c09db307169115541f827ec8c21aa270700000012401340"]`,
+			result: func(e *executor) interface{} { return &result.Invoke{} },
+			check: func(t *testing.T, e *executor, inv interface{}) {
+				res, ok := inv.(*result.Invoke)
+				require.True(t, ok)
+				assert.Equal(t, "HALT", res.State)
+				require.Equal(t, 1, len(res.Stack))
+				require.Equal(t, int64(1), res.Stack[0].Value)
+			},
+		},
+		{
+			name:   "positive, bad hashes witness",
+			params: `["5707000c14010c030e05060c0d020e0f0d030e070900000000db307068115541f827ec8c21aa270700000011400c140d0f03020900020103070304050201000e060c09db307169115541f827ec8c21aa270700000012401340",["0x0000000009070e030d0f0e020d0c06050e030c02"]]`,
+			result: func(e *executor) interface{} { return &result.Invoke{} },
+			check: func(t *testing.T, e *executor, inv interface{}) {
+				res, ok := inv.(*result.Invoke)
+				require.True(t, ok)
+				assert.Equal(t, "HALT", res.State)
+				assert.Equal(t, 1, len(res.Stack))
+				assert.Equal(t, int64(1), res.Stack[0].Value)
+			},
+		},
 		{
 			name:   "no params",
 			params: `[]`,
diff --git a/pkg/rpc/server/testdata/test_verify.avm b/pkg/rpc/server/testdata/test_verify.avm
new file mode 100755
index 000000000..100b20621
Binary files /dev/null and b/pkg/rpc/server/testdata/test_verify.avm differ
diff --git a/pkg/rpc/server/testdata/test_verify.go b/pkg/rpc/server/testdata/test_verify.go
new file mode 100644
index 000000000..1587e14da
--- /dev/null
+++ b/pkg/rpc/server/testdata/test_verify.go
@@ -0,0 +1,17 @@
+package testdata
+
+import "github.com/nspcc-dev/neo-go/pkg/interop/runtime"
+
+// This contract is used to test `invokescript` and `invokefunction` RPC-calls
+func Main() int {
+	// h1 and h2 are just random uint160 hashes
+	h1 := []byte{1, 12, 3, 14, 5, 6, 12, 13, 2, 14, 15, 13, 3, 14, 7, 9, 0, 0, 0, 0}
+	if !runtime.CheckWitness(h1) {
+		return 1
+	}
+	h2 := []byte{13, 15, 3, 2, 9, 0, 2, 1, 3, 7, 3, 4, 5, 2, 1, 0, 14, 6, 12, 9}
+	if !runtime.CheckWitness(h2) {
+		return 2
+	}
+	return 3
+}