WASHINGTON — Clashes are continuing with Islamic State fighters in eastern Syria, United States military officials said on Friday after the White House claimed that American-backed forces had retaken the extremist group’s final sliver of territory.

Sarah Huckabee Sanders, the White House press secretary, told reporters aboard Air Force One that the Islamic State’s caliphate in Syria had been “100 percent eliminated.” She said Acting Defense Secretary Patrick M. Shanahan had briefed President Trump during the flight.

Mr. Trump has declared the Islamic State’s defeat several times in recent weeks. Each time, Pentagon officials have gingerly tried to clarify that the group’s remnants remain hunkered down — first in the town of Hajin and now outside the small village of Baghuz on the Syria-Iraq border.

Ms. Sanders told reporters to refer questions to the Pentagon, but the Defense Department declined a request for comment.