diff --git a/core/state_transition.go b/core/state_transition.go
index b51dcc375..60aad1d2b 100644
--- a/core/state_transition.go
+++ b/core/state_transition.go
@@ -368,12 +368,18 @@ func (st *StateTransition) TransitionDb() (*ExecutionResult, error) {
 		return nil, err
 	}
 	if st.gas < gas {
-		return nil, fmt.Errorf("%w: have %d, want %d", ErrIntrinsicGas, st.gas, gas)
+		// Allow L1 message transactions to be included in the block but fail during execution,
+		// instead of rejecting them outright at this point.
+		if st.msg.IsL1MessageTx() {
+			gas = st.gas
+		} else {
+			return nil, fmt.Errorf("%w: have %d, want %d", ErrIntrinsicGas, st.gas, gas)
+		}
 	}
 	st.gas -= gas
 
 	// Check clause 6
-	if msg.Value().Sign() > 0 && !st.evm.Context.CanTransfer(st.state, msg.From(), msg.Value()) {
+	if msg.Value().Sign() > 0 && !msg.IsL1MessageTx() && !st.evm.Context.CanTransfer(st.state, msg.From(), msg.Value()) {
 		return nil, fmt.Errorf("%w: address %v", ErrInsufficientFundsForTransfer, msg.From().Hex())
 	}