LONDON — After several months of scandal within Britain’s opposition Labour Party over its handling of anti-Semitism in its ranks, investigators in London said on Friday that they have opened a criminal inquiry into accusations that some party members posted anti-Semitic threats online.

The Metropolitan Police commissioner, Cressida Dick, said in an interview with BBC Radio 4 that officers were looking into online posts by Labour members that amounted to more than just offensive comments. The police are consulting with prosecutors at this stage of the investigation.

“We are now investigating some of that material because it appears there may have been a crime committed,” she said.

Ms. Dick said that the Labour Party itself was not under investigation, and that while she hoped political parties policed themselves on issues like anti-Semitism, officers had an obligation to look into such allegations.