Preheat stove top or gas grill to high heat. Stir together butter, onion, and dill ingredients in small bowl. Brush tuna steaks with olive oil and coat with cracked pepper.
Place tuna steaks on grill and cook to desired doneness, turning once: 2 minutes on each side for rare center; 3 to 5 minutes each side for medium center; 5 to 6 minutes each side for well-done center.
Serve with topped with a dollop of dill-onion butter.