Once one of Britain’s best-known politicians, Mr. Livingstone was criticized in 2016 for telling the BBC that in 1932 Hitler had championed Jewish emigration to Israel and was “supporting Zionism before he went mad and ended up killing six million Jews.”

On Monday, Mr. Livingstone rejected claims that he had brought the Labour Party into disrepute and said he was not guilty of anti-Semitism, while acknowledging that his comments had upset Jews and offended others.

“I am truly sorry for that,” he said in a statement.

Mr. Corbyn described Mr. Livingstone’s departure as “sad after such a long and vital contribution to London and progressive politics,” but added that it “was the right thing to do.”

Under Mr. Corbyn’s leadership the Labour Party has been accused of failing to root out anti-Semitism within its ranks. Demonstrators gathered outside Parliament in March, asserting that Jews no longer felt welcome in the party.

That followed the revelation that, in 2012, Mr. Corbyn had endorsed a mural that was widely considered anti-Semitic — something for which he has since apologized.