diff --git a/src/cmd/compile/internal/gc/const.go b/src/cmd/compile/internal/gc/const.go
index 510b1cd15d..3666ddbaa0 100644
--- a/src/cmd/compile/internal/gc/const.go
+++ b/src/cmd/compile/internal/gc/const.go
@@ -591,7 +591,7 @@ func evconst(n *Node) {
 			setconst(n, shiftOp(nl.Val(), op, nr.Val()))
 		}
 
-	case OCONV:
+	case OCONV, ORUNESTR:
 		if okforconst[n.Type.Etype] && nl.Op == OLITERAL {
 			setconst(n, convertVal(nl.Val(), n.Type, true))
 		}
diff --git a/test/const.go b/test/const.go
index 3f4956497e..f8aa1dd9ab 100644
--- a/test/const.go
+++ b/test/const.go
@@ -24,6 +24,10 @@ const (
 
 	ctrue  = true
 	cfalse = !ctrue
+
+	// Issue #34563
+	_ = string(int(123))
+	_ = string(rune(456))
 )
 
 const (