Conservatives pushing for Theresa May to categorically rule out a no-deal Brexit in parliament this week have urged their colleagues not to be bought off by vague promises of a future vote on whether to extend article 50.

May is expected to make a last-ditch attempt to avoid a cabinet rebellion, before a vote on Wednesday on a cross-party amendment laid by the Tory Oliver Letwin and Labour’s Yvette Cooper that would in effect rule out a no-deal scenario.

The prime minister’s most likely option is a pledge to let MPs vote on delaying Brexit for a short time if she does renegotiate her withdrawal deal and win support for it before 12 March.

However, those leading efforts to get a no-deal Brexit taken off the table said the proposal was “absolutely not good enough”, as they urged cabinet and junior ministers threatening to resign over the issue to hold their nerve.

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They believe they have enough promises from MPs to pass the Cooper-Letwin amendment, especially now the Labour frontbench has pledged its support. But the group is still keen to secure the backing of cabinet ministers and junior ministers who have threatened to defy the government whip.

Three cabinet ministers – Amber Rudd, David Gauke and Greg Clark – threw down the gauntlet to May at the weekend as they urged her to remove the possibility of a no-deal Brexit. It is understood they are all planning to listen carefully to what May has to offer on Tuesday, raising the possibility that they will back away from having to resign or be sacked. One alternative is that May offers a free vote to allow ministers to vote for the Cooper-Letwin amendment without having to leave their government positions.

Three other ministers have urged May to take a no-deal Brexit off the table. Writing in the Daily Mail, Richard Harrington, Claire Perry and Margot James said the government should extend article 50 to avoid leaving with no agreement on 29 March. The paper also claimed that 15 ministers would be ready to resign to stop no deal.

May insisted on Tuesday that she did not want a delay to Brexit but it was discussed in meetings with Angela Merkel, the German chancellor, and Donald Tusk, the European council president, at a summit in the Egyptian resort of Sharm el-Sheikh.

“An extension to article 50, a delay in this process, doesn’t deliver a decision in parliament, it doesn’t deliver a deal,” she said at a separate press conference. “All it does is precisely what the word ‘delay’ says. Any extension of article 50 isn’t addressing the issues.

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“We have it within our grasp. I’ve had a real sense from the meetings I’ve had here and the conversations I’ve had in recent days that we can achieve that deal. It’s within our grasp to leave with a deal on 29 March and that’s where all of my energies are going to be focused.”

However, even some of her most loyal supporters in parliament told the Guardian that a delay to Brexit was “pretty much inevitable”.

“There is no way we would get the legislation through in time now anyway. It’s not really clear why she is still insisting we can. What we need is some pitch-rolling for a short delay,” one MP said.

Backers of the Cooper-Letwin amendment said it was still crucial to make sure a no-deal Brexit is ruled out this week.

Antoinette Sandbach, a Conservative MP who supports the Cooper-Letwin amendment, said: “No deal must be ruled out this week. Anything else is frankly irresponsible for people trying to plan businesses and their lives.”

Dominic Grieve, the former attorney general under David Cameron, said the suggestion of a short, time-limited delay to Brexit if May’s deal does not pass was “absolutely not good enough”.

Nick Boles, writing in the Evening Standard, said it was “the last chance saloon” and warned his colleagues not to fall for the prime minister’s concession if it falls short of ruling out a no-deal Brexit.

Some supporters of May’s deal in parliament – known as the Brexit delivery group – had planned to table a rival amendment in favour of a time-limited delay but they are not confident of enough support for it to be chosen and may not pursue it.

Among European politicians, several warned that time was running out and reflected gloomily on May’s chances of winning enough support from hardline Eurosceptic Tories and the Democratic Unionist party to get her deal through parliament. After delaying the meaningful vote on the deal, previously scheduled for this week, May has said she will return to the Commons on 12 March to put it to MPs.

Meanwhile, Donald Tusk, the European Council president, warned that May was unlikely to get her revised deal through the House of Commons as it currently stands, leaving the UK with the option of “a chaotic Brexit” or an extension of its membership of the EU beyond 29 March.

The European council president revealed that he and the prime minister had walked through the legal process that would need to be followed to delay Brexit.

As she seeks to shorten the timetable for approval of a Brexit deal before 29 March, May signalled it could be possible for MPs to vote on an agreement before it has been formally approved on 22 March by the EU.

“It would be possible to do it either way and I would hope that we have that meaningful vote by the 12th,” she said.

The EU’s chief negotiator, Michel Barnier, is due to re-engage with the British team, including Downing Street’s senior Brexit adviser, Olly Robbins, the Brexit secretary, Stephen Barclay, and Geoffrey Cox, the attorney general, in Brussels on Tuesday.

The two sides are drafting text that puts previous assurances of the temporary nature of the backstop, contained in letters from Tusk and Juncker late last year, into a legally-binding form.

The Dutch prime minister, Mark Rutte, who also met May for talks in the Red Sea resort of Sharm el-Sheikh, said he feared that the UK was “sleepwalking” to a no-deal Brexit. He warned May that the EU was determined to avoid granting a short extension only to have to repeatedly revisit the issue due to a lack of direction in London.