In 8-inch square (2-quart) glass baking dish, combine all ingredients except tuna steaks; mix well. Add tuna; turn to coat. Let stand while grill is heating.
Heat gas or charcoal grill. When grill is heated, remove tuna from soy sauce mixture; reserve mixture. Place tuna on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cover grill; cook 10 to 12 minutes or until fish flakes easily with fork and is opaque in center, turning once and brushing frequently with soy sauce mixture.
Bring any remaining soy sauce mixture to a boil in small saucepan. Serve tuna with warm soy sauce mixture.