Labour has accused Donald Trump’s top official, Mike Pompeo, of trying to stop Jeremy Corbyn becoming prime minister, after he was caught on tape telling Jewish leaders that he would “push back” against the party’s leadership.

In a recording leaked to the Washington Post, the US secretary of state was asked what he would do if Corbyn were to be elected as prime minister, after sustained criticism over Labour’s handling of accusations of antisemitism within the party.

The questioner said: “Would you be willing to work with us to take on actions if life becomes very difficult for Jews in the UK?” In response, Pompeo appeared to suggest that he would seek to intervene in the debate before Corbyn had a chance to become prime minister.

“It could be that Mr Corbyn manages to run the gauntlet and get elected,” he said on the recording. “It’s possible. You should know, we won’t wait for him to do those things to begin to push back. We will do our level best. It’s too risky and too important and too hard once it’s already happened.”

A Labour spokesman said: “President Trump and his officials’ attempts to decide who will be Britain’s next prime minister are an entirely unacceptable interference in the UK’s democracy.” He added that the party was “fully committed to the support, defence and celebration of the Jewish community and is implacably opposed to antisemitism in any form”.

Pompeo’s comments emerged after Trump turned down Corbyn’s request for a meeting during his state visit to the UK last week, saying the leader was “somewhat of a negative force”. Corbyn joined protests outside Trump’s press conference with Theresa May, where he pledged to oppose the US president’s drive for greater access for US health companies to NHS contracts.

The comments come at a time when Corbyn’s team are nervous about the latest attempts to oust him from within the party over the issues of antisemitism and Brexit, after several senior figures came out in support of a second referendum.

Shadow cabinet sources said the leadership was preparing to take on Tom Watson and his supporters after his vocal campaign to soften Corbyn’s Brexit position, with moves under way to generate momentum in favour of a new deputy leadership election.

There is growing talk about the possibility of the party’s rules being changed to create a second deputy leader, alongside Watson, but also the possibility of a new deputy leadership contest altogether. Some Corbyn supporters are circulating motions against Watson around local constituency Labour parties and a grassroots petition against the deputy leader has got about 26,000 signatures so far.

One shadow cabinet minister said they believed the leadership wanted to make the shadow cabinet less in favour of a second referendum. As part of this, Corbyn’s team considered swapping Emily Thornberry, the shadow foreign secretary, with Diane Abbott, the home secretary, over her support for a second referendum and wider foreign policy issues.

However, it is understood that Thornberry has more recently been assured that she will not be moved and that Abbott was opposed to such a plan anyway, which would make the move difficult to carry out without a public battle.

A Labour source said there were no plans at all for a reshuffle and dismissed speculation about moves within the top team as mischief-making.

Talk of a reshuffle was sparked when Thornberry was dropped as Corbyn’s usual stand-in for prime minister’s questions this week after speaking out about Labour’s strategy for the European elections. On polling day last month, Thornberry said Labour was “not clear on the one single thing that people wanted to hear”. She was replaced at the dispatch box by Rebecca Long-Bailey, a rising star on the left of the party and a staunch Corbyn loyalist.