A Ukrainian counteroffensive appears to have driven Russian forces back from Kharkiv, Ukraine’s second-largest city, The Washington Post reports.

A senior U.S. defense official told reporters on Friday that Ukraine had reclaimed towns and villages in the vicinity of Kharkiv, forcing Russian troops back toward Ukraine’s northern border.

The U.S.-based Institute for the Study of War assessed that Ukraine “appears to have won the Battle of Kharkiv” and that Russian high command has “likely decided to withdraw fully” due to Ukrainian counterattacks and the “limited availability of reinforcements.”

The counteroffensive, which began earlier this month, drove Russian forces out of artillery range of Kharkiv for the first time since the early days of the war and could threaten the supply lines sustaining Russia’s main campaign in the Donbas. BBC correspondent Quentin Sommerville described the battles around Kharkiv as “a game of hawk and mouse,” in which both sides deployed drones to identify targets for artillery.

The Institute for the Study of War suggested Friday that, as decisive victory over Ukraine slips out of reach, “Russian President Vladimir Putin likely intends to annex occupied southern and eastern Ukraine directly into the Russian Federation in the coming months.”

The ISW also predicted that Putin will “state, directly or obliquely, that Russian doctrine permitting the use of nuclear weapons to defend Russian territory applies to those newly annexed territories.”