Theresa May will hold a peace summit for her warring cabinet to finalise the Brexit white paper at her country retreat in Chequers – but it will not take place until after the European Council summit later this month.

Ministers will be summoned to the prime minister’s country retreat “soon” after the EU summit on the last weekend in June. David Davis, who is drafting the document, had initially hoped the white paper on the UK’s post-Brexit future would be published before the European Council summit in a fortnight’s time.

May held a long private meeting with David Davis on Thursday as her Brexit secretary looked like he was on the brink of resignation. He is understood to have expressed a litany of frustrations in the meeting, not only over the “backstop” agreement on the Northern Irish border, but also the delay in publishing the white paper.

In the tense compromise talks on Thursday, May agreed to the Chequers’ summit as a way of pushing the process forward. Downing Street was determined there should be no white paper before the June summit, where some technical matters on the divorce deal have to be resolved.

“We wanted to publish something that showed the breadth of our ambition,” one Downing Street source said. “David Davis wants to get on, the prime minister wants to get on, and we all want to get the best results.”

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The argument over the white paper revives the differences between Brexiters and remainers that provoked the last Chequers showdown in February, when the cabinet agreed on “ambitious managed divergence” for post-Brexit trading arrangements.

May placated Davis on Thursday by offering to move the white paper process on and insert an end date into the UK’s plan for a customs backstop.

However, the peace was shortlived after explosive comments were leaked from foreign secretary Boris Johnson at a private dinner, attacking the chancellor Philip Hammond. Speaking to the Conservative Way Forward campaign group, Johnson said the Treasury was “the heart of remain” and said concerns over the Northern Irish border were “allowing the tail to wag the dog”.

May, who was en route to the G7 summit in Canada when Johnson’s words were leaked, defended him. “Boris has strong views on Brexit but so do I,” she told Channel 4 News. “If you look at the process of these negotiations – nobody ever said it was going to be easy.”

Behind the scenes, however, there was considerable anger that the foreign secretary had dismissed the border problem. One source described the remarks as “very, very badly judged and unbecoming”.

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Hammond hit back on Friday: “My experience has been that ... a collaborative approach ... is generally more productive than a confrontational approach.”

Meanwhile, Conservative pro-EU rebels are quietly considering their approach to a government proposal aimed at averting defeat on the EU withdrawal bill next week. The government has proposed a 28-day breathing space if parliament rejects Theresa May’s Brexit deal.

The MPs have held their fire thus far in response to the compromise offer, though one said they believed it to be insubstantial. The amendment would bind the offer of a parliamentary vote into law, but remove the timetable laid down in a Lords amendment of how the government should respond to any defeat.

A spokesperson for the Department for Exiting the European Union said: “Our amendment removes parliament’s ability to direct the government in relation to negotiations, which would set a huge constitutional precedent in terms of which branch of the state hold prerogative to act in the international sphere.”