Meanwhile, a senior MP supporting Smith claimed there was an overwhelming consensus that only one candidate should emerge, and warned that currently supportive MPs would not give Eagle their nomination if she did not swiftly recognise the situation.
“Angela needs to be very careful,” said the source. “It is not a question of who deserves to be leader; it is about the best possible candidate to beat Jeremy.”
The row blew up following Smith’s public declaration in a BBC interview on Friday that Corbyn should be presented with just one challenger. The formal window for MPs to declare their support for a leadership candidate starts on Monday and finishes on Wednesday.
Smith suggested in his interview that either the deputy leader, Labour’s national executive committee or the parliamentary party could devise a process to whittle the two challengers down if they both had the required 51 nominations to go on the ballot paper.
However, sources close to Eagle immediately dismissed that suggestion, pointed out that the candidate who won the fewest nominations became leader last year and that she was “in it to win it”.
One angry MP backing Eagle described Smith’s suggestion as an attempt to “bully Angela into some sort of corner”.
He added: “Angela didn’t step aside for Jeremy and she isn’t going to do so for Owen. If he wants to stay on, it is a contest. Bring it on. Colleagues are sick of these sneaky tactics. They need to pipe down.”
A source close to Smith, who launches his campaign on Sunday, said that Smith was running a “comradely, magnanimous campaign” and that he was merely offering to engage with any process devised to choose between the two MPs in the interest of the party.
It is understood that Smith would be willing to stand aside if Eagle – who was the first to declare her intention to challenge the Labour leader – could show that she had a greater number of nominations from MPs. Smith is currently said to have the firm support of around 90 MPs and MEPs, which his supporters believe is around 35 nominations more than Eagle. A spokesman for Eagle dismissed the claim but declined to comment on the level of her support.
The row between the candidates’ camps emerged as the deputy leader, Tom Watson, in an article in the Observer, slams Corbyn, who is in favour of unilateral disarmament, saying those who vote against the renewal of Trident in parliament on Monday are putting “tens of thousands of defence engineers out of work, many of them members of Unite and GMB”.
Watson adds that those who abstain are “abdicating responsibility” on an issue of strategic defence.
Also writing in the Observer, Eagle, whose constituency office windows were smashed by a brick last week, turns on Corbyn, claiming that by settling into “a sectarian comfort zone”, he had provoked “personal attacks on MPs, [and] a string of death and rape threats and bricks through windows”.
She adds that progressive politics means reaching out to all parts of society. “Politics is not about taking sides – or, at least, it shouldn’t be,” she writes. On Saturday evening Corbyn tweeted a code of conduct for the leadership contest, insisting that no one should feel intimidated at hustings, at home or in their office.
Meanwhile in a wide-ranging interview with the Observer, Smith says that he agreed with the decision by Labour’s governing body, the national executive committee, to put Corbyn automatically on the ballot paper as it is what the members would expect.
The former shadow work and pensions secretary, however, reveals he had suggested to Corbyn that he could become president or chair of Labour, in return for standing down.
Smith, who has promised that Labour will campaign for a second referendum on the terms of Brexit, further claims that “in his heart of hearts” he believes that a credible Labour party under his leadership could still keep Britain in the EU despite last month’s vote.
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