The shadow chancellor, John McDonnell, has entered the row over the outspoken Labour leadership critic Luciana Berger by saying all she has to do is denounce breakaway stories and the deselection threat against her will go away.

McDonnell said it was his understanding the Liverpool Wavertree MP faced a confidence vote not because she stood up to antisemitism in the party, but because she has been associated with setting up a breakaway party.

“Luciana has been associated in the media with a breakaway party … the media have asked her to deny that and she hasn’t been clear on that. So, my advice on all of this is for Luciana to just put this issue to bed,” he said on BBC Radio 4’s Today programme.

Facebook Twitter Pinterest Luciana Berger has had motions of no confidence tabled against her. Photograph: Jonathan Hordle/ITV/Rex/Shutterstock

But critics accused the shadow chancellor of making veiled threats, claiming Berger was being targeted for speaking out against antisemitism in the party.

Chuka Umunna, the MP for Streatham, said: “So a victim of outrageous racism in Labour must promise she will not walk because of that racism and then this can all go away. How about demanding her CLP treats her with the respect she deserves. How about the party deals with that racism? Words fail me. Totally unacceptable.”

Berger has called an extraordinary meeting of her local party after motions of no confidence were tabled against her. Agendas have been issued to 1,700 members of the Liverpool Wavertree constituency Labour party with two motions that both call for votes of no confidence in Berger.

The motion says that instead of fighting for a Labour government, Berger “is continually using the media to criticise the man we all want to be prime minister”.

McDonnell said the vote had nothing to do with antisemitism. “If people are doing it [the no-confidence vote] because Luciana stood up to antisemitism then that is wrong. But Luciana has been in the media associated with a breakaway party and has not been clear in stating she rejects that,” he said.

“Any elements of antisemitism in the Labour party, we will deal with them. Full stop.”

The move against Berger came after she joined other MPs at a meeting of the parliamentary Labour party on Monday in calling for details of the party’s efforts to tackle antisemitism to be released.

Berger’s stance on antisemitism has led to her facing a torrent of abuse from online trolls, and she required a police escort at last year’s Labour party conference after receiving death threats.

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On Saturday night, three MPs widely rumoured to be involved in a breakaway movement in the Labour party – Angela Smith, Chris Leslie and Berger – refused to be drawn into talk of a split, and insisted they were focused on opposing Brexit. But they did not deny that moves could be made by the spring or early summer.