"Well, I'm not going to put a timetable on it because, as you know, war is unpredictable," Sullivan told in an interview with a American TV channel.
Sullivan said that events currently taking place on the battlefield will have a decisive influence on how the dialogue on peace plays out. Ultimately, however, the conflict in Ukraine will end at the negotiating table, he added.
The official noted that Washington intended to help Kiev make as much progress as possible on the battlefield to enable it to take the most advantageous position at the table of future peace talks.
"We do believe that this counteroffensive will allow Ukraine to take strategically significant territory back from Russia," Sullivan said.
On Friday, White House Strategic Communications Coordinator John Kirby said the conflict in Ukraine is not going to end with a "simple withdrawal" of Russian forces from contested areas.
Western countries have been supplying Ukraine with various types of weapons, including air defense missiles, multiple launch rocket systems, tanks, self-propelled artillery and anti-aircraft guns since Russia launched its special military operation in Ukraine over a year ago. Moscow has warned that the arms deliveries do not contribute to a peaceful solution and further escalate the conflict, risking full NATO involvement.