LONDON — President Trump offered little succor to the authorities in Britain on Wednesday in a growing dispute over an American woman who fled the country using diplomatic immunity after being involved in a road crash that left a teenage motorcyclist dead.

Prime Minister Boris Johnson of Britain had said that he would appeal directly to the president for the return of the woman, Anne Sacoolas, a diplomat’s wife. The police in Northamptonshire, England, suspect her of being the driver of a car that they say was on the wrong side of the road when it collided with a motorcycle ridden by Harry Dunn, 19.

When Mr. Johnson raised the case in a phone call on Wednesday, according to a statement from the prime minister’s office, Mr. Trump expressed his condolences to Mr. Dunn’s family and “agreed to work together to find a way forward,” but the statement made no mention of withdrawing diplomatic immunity or any other specific remedy.

The case has created diplomatic and political complications for Mr. Johnson, who needs good relations with Mr. Trump to try to secure a trade deal from the United States after Britain leaves the European Union.