“We are unhappy with the pervasive anti-Semitism that still remains on the left but continue to remain very much involved because we are committed to a better world and a better left,” the statement said.

Since his election as Labour leader, Mr. Corbyn has been at war with a sizable section of his party, some of whom say he lacks credibility as a potential prime minister. However, he has brought thousands of new supporters to the party, confounded critics by running a much more successful election campaign last year than expected and has since tightened his control of the Labour apparatus.

Yet, even if Mr. Corbyn is in a position of internal strength, the anti-Semitism dispute, along with his reluctance to blame Russia for the poisoning of a former spy in Salisbury, England, has rekindled debate about his leadership.

Schooled in left-wing, protest politics, Mr. Corbyn’s worldview seems to have remained much as it was when he entered Parliament in 1983, at the beginning of a long period on the fringes of the Labour Party.

“His has an implacable, binary, worldview,” Professor Fielding said. “He sees Israel as Zionist, and Zionism as part of imperialism, and imperialism as the part of the enemy.”

The latest questions over anti-Semitism began more than a week ago when a Labour lawmaker, Luciana Berger, asked questions about Mr. Corbyn’s endorsement, in 2012, of a campaign to save a mural in east London that caricatured Jewish bankers playing Monopoly on the backs of the poor. Mr. Corbyn’s office took hours to produce an equivocal response, before eventually issuing an apology.

A protest by Jewish groups outside Parliament was followed by the resignation of Christine Shawcroft, the chair of Labour’s internal disputes panel, after the leak of an email suggesting that she had supported a local candidate who was suspended over accusations of anti-Semitism.