Theresa May has written to Donald Tusk to ask for Brexit to be delayed until 30 June while she battles to win cross-party agreement on a way forward.

Rather than the year-long flexible extension to article 50 recommended by the European council president, the prime minister suggested 30 June as the new departure date, but with an option to leave earlier if the necessary legislation has been passed.

That is the same date requested by the government last month but rejected by EU leaders in Brussels. Unless a new date is signed off at an emergency EU summit on Wednesday, Britain is due to leave without a deal on 12 April.

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In the letter, drafted after a second day of talks with Labour, May said both parties accepted the need to pass the legally binding withdrawal agreement but had not reached consensus on the future relationship.

If that was not possible, May said, she hoped to agree with Labour a process for parliament to choose between possible options, the outcome of which both sides would promise to accept.

That could allow parliament to ratify the deal, pass the necessary legislation and leave before 22 May, meaning the UK would avoid participating in European parliament elections, the prime minister added.

But she conceded the government would be “under a legal obligation” to hold those elections if it had not left in time.

“The government will want to agree a timetable for ratification that allows the United Kingdom to withdraw from the EU before 23 May 2019 and therefore cancel the European parliament elections, but will continue to make responsible preparations to hold the elections should this not prove possible,” she said.

Asked why May was seeking a date that had already been rejected, her spokesman said there were “different circumstances now” to when she requested 30 June before the last European summit, and that the prime minister had pledged to not seek an extension beyond that date.

Her spokesman declined to say whether May would definitely refuse any extension beyond then. He said: “She set out today that she’s seeking a date of 30 June – let’s not get ahead of that. That’s what she’s focused on achieving.”

The request for a short extension is likely to exasperate remain-supporting cabinet ministers who have urged her to seek a longer delay. But May would have faced a backlash from leavers if she had requested a longer period. In a long cabinet meeting this week, ministers made several strongly worded arguments against any extension at all.

Jacob Rees-Mogg, the chair of the backbench European Research Group, tweeted that if the UK were forced to remain an EU member for a longer period, it should be as obstructive as possible.

Jacob Rees-Mogg (@Jacob_Rees_Mogg) If a long extension leaves us stuck in the EU we should be as difficult as possible. We could veto any increase in the budget, obstruct the putative EU army and block Mr Macron’s integrationist schemes.

In her letter, the prime minister wrote: “The United Kingdom is seeking a further extension … [and] proposes that this period should end on 30 June 2019. If the parties are able to ratify before this date, the government proposes that the period should be terminated early.”

Talks between the government and Labour are due to resume on Friday morning. Sources on both sides said discussions on Thursday had been serious and detailed, but the government had not yet made it clear how it could be willing to compromise.

Labour’s deputy leader, Tom Watson, said he would face “difficulty” among the party’s MPs if he sought to agree a deal without a referendum attached.

“I am a reluctant convert to the idea of a confirmatory ballot. I genuinely believe it was parliament’s job to sort this out and there should have been a meaningful vote, but in two years we have just hit cul-de-sac after cul-de-sac, so clearly we went into the discussions with the idea that there would be a confirmatory ballot,” he told BBC Radio 4’s Today programme.

Facebook Twitter Pinterest Labour’s Tom Watson speaks at the Put it to the People march in London last month. Photograph: Hugo Philpott/UPI/Barcroft Images

Tusk is pushing the EU27 to offer a one-year “flexible” extension to article 50, with an option to leave earlier once the withdrawal agreement is ratified by parliament. He is said to have described the plan as “the only reasonable way out”.

Tusk was due to tell leaders at a summit on Wednesday that the “flextension” would avoid them having to consider extra delays every few weeks. The EU27 would need to unanimously agree to the plan.

Tusk is determined to give Downing Street as much flexibility as possible to avoid any suggestion that Brussels is seeking to trap Britain in the EU. But the prime minister’s suggestion of 30 June is unlikely to appeal to the EU27.

While May said in her letter that she would hold European elections should the UK remain in the EU past 22 May, the proposal would create yet another cliff-edge date in the summer.

The EU would be in a transition phase, with the terms of Jean-Claude Juncker, the European commission president, and Tusk coming to an end, and it would open up the possibility of leaders being dragged into making serial extensions over time.

A senior official said Tusk told senior figures on Thursday evening that the flextension was the best solution for both sides.

“The only reasonable way out would be a long but flexible extension,” Tusk reportedly said. “I would call it a ‘flextension’. How would it work in practice? We could give the UK a year-long extension, automatically terminated once the withdrawal agreement has been accepted and ratified by the House of Commons.”

Facebook Twitter Pinterest Emmanuel Macron has grown increasingly frustrated at the failure of British politicians to agree a post-Brexit plan. Photograph: Jean Catuffe/Getty Images

The failure of the UK parliament to coalesce around a post-Brexit vision will be a source of frustration for Emmanuel Macron, the French president, who has insisted the UK must have a “credible plan” for the EU to offer any further extension.

EU sources said the plan would, however, offer the reassurance that Britain would be making its own fortune and not dragging Brussels into its crisis.

The UK would have to hold elections to the European parliament on 23 May under the Tusk plan, but British MEPs would leave the chamber once the UK had departed from the bloc. MEPs from the other 27 member states would then step in, sources suggested.

The attorney general, Geoffrey Cox, said in an interview with the BBC that he thought the offer from the EU was “likely to be a long one” and would have to be accepted by Downing Street.

The current legal position is that the UK will leave the EU at 11pm BST on 12 April.