Jeremy Corbyn has been made the subject of an official complaint to the Labour party over his suggestion in 2013 that some British Zionists do not understand “English irony”.

The Labour leader has since sought to clarify the remarks, which have ensured that the party remains embroiled in a row over its attitude towards antisemitism that has dragged on for months. Some MPs and peers are understood to be discussing the possibility of a kind of split, with one faction awaiting the outcome of the party’s handling of Brexit to decide what to do next.

Speaking at a London conference five years ago, Corbyn was recorded saying that a group of Zionists had no sense of irony, despite “having lived in this country for a very long time”. The comments angered some of his MPs and led one to say she felt “unwelcome in my own party”.

Corbyn said he had used the term Zionist “in the accurate political sense and not as a euphemism for Jewish people” and that he was defending the Palestinian ambassador from “deliberate misrepresentations” by people “for whom English was a first language, when it isn’t for the ambassador”. However, he also committed to being “more careful” with the language he used.

The party was delivered an official complaint on Saturday about the comments by the Labour Against Antisemitism group, which said it was reporting Corbyn “for antisemitism and for bringing the party into disrepute”.

It comes after a recently departed Labour staffer involved in investigating complaints raised concerns about the remarks. Dan Hogan, a former member of Labour’s governance and legal unit, said on Twitter: “If Corbyn were any other member, he would have been suspended and investigated, and the [National Executive Committee] would nod through the bulging report on his offences. He would join the long queue of other awful people waiting for a disciplinary hearing with the National Constitutional Committee.”

Euan Philipps, a spokesperson for Labour Against Antisemitism, said: “The leader of our party must be subjected to the same scrutiny and procedures as any other member. It is time for the Labour party to show it is serious about tackling antisemitism by immediately suspending Mr Corbyn and launching a full and independent investigation into his conduct.”

Labour insiders have claimed that the number of people working on party disputes has actually fallen, despite the crisis over antisemitism and an apparent backlog of complaints.

The row has reopened deep divisions within Labour, despite the party still commanding 40% support in the polls. Jewish Labour MP Luciana Berger said Corbyn’s 2013 remarks were “inexcusable comments” which made her feel “unwelcome in my own party”. She received support from fellow MPs. However, Corbyn’s supporters insist his comments have been misinterpreted.

The infighting has led to open talk among some MPs about whether or not they feel they can stay in the party as a result of their disagreements with the leadership. Some said that it was now highly likely that some would opt to sit as independent MPs at some point – an option already taken by former Labour MP and Corbyn critic, John Woodcock.

The next fortnight will be significant in the party’s handling of antisemitism. It is set to decide whether or not to adopt the full International Holocaust Remembrance Alliance definition of antisemitism, as well as its accompanying examples. Doing so may help defuse the row, though Corbyn has said he wants to ensure that legitimate criticism of Israel is not damaged in the process.

It sets the scene for a fractious Labour conference next month, when the party will also have to confront splits over its position on Brexit. In the meantime, some MPs are not sure how to react when they return to Westminster after the summer. “Luciana reflected this well,” said one. “Some of us are being made to feel unwelcome and uncomfortable.”

While one party source said they were not aware of the complaint, a Labour spokesperson said: “The Labour party’s complaints procedure operates confidentially in the interests of fairness to all concerned. This is to ensure protection of the personal data both for any members who make complaints, and for those to whom complaints relate. This enables procedures to be followed properly. Therefore we do not comment on individual cases.”