A Brexit deal by the scheduled withdrawal date of March 29 is “within our grasp,” Theresa May has insisted as she set her face against putting back exit day.

Her comments came just moments after Donald Tusk described extending the Article 50 process as a “rational solution” to the current UK-EU impasse, warning that the only alternative if MPs could not agree a deal, was "a chaotic Brexit".

The European Council President revealed he had discussed the legal and procedural process for extending the withdrawal talks when he met the Prime Minister in Egypt yesterday.

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EU officials are said to be considering the option of a delay to exit day not just for a few months as some UK ministers have suggested but until 2021 so that more talks can eliminate the need for the contentious Irish backstop.

Pressure is mounting at Westminster from within and outwith the Conservative Party and, indeed, from within the Government itself, for Mrs May to delay withdrawal as MPs prepare to vote for such a proposition tabled in a binding amendment to Wednesday’s debate in the Commons by Labour’s Yvette Cooper.

But, speaking during a press conference at the EU-Arab summit in Sharm el-Sheikh, the PM insisted extending Article 50 would not address the issues facing Britain over its departure from the EU.

“A delay in this process does not deliver a decision in Parliament, it doesn’t deliver a deal; what it does is precisely what the word says,” declared Mrs May, who has had a raft of meetings at the Red Sea resort, including with Germany’s Angela Merkel, Ireland’s Leo Varadkar and the European Commission President Jean-Claude Juncker.

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She told journalists: “I have a real sense from the meetings I have had here, conversations I have had with EU leaders in recent days…we can achieve that deal. It’s within our grasp to leave with a deal on March 29 and that’s where all our energies are going to be focused.”

The PM, who has put off having a meaningful vote this week but promised one by March 12, admitted there was “still more work to do”.

But she noted: “What I have sensed in all of my conversations with my fellow leaders both here in Sharm el-Sheikh and in recent days is a real determination to find a way through, which allows the UK to leave the EU in a smooth and orderly way with a deal.”

Asked if Cabinet ministers Amber Rudd, Greg Clark and David Gauke, who have suggested they could back Ms Cooper’s amendment, would have to resign if they did so, Mrs May brushed aside the question.

She said: “First of all, we have not laid the motion for Wednesday yet, we have not had amendments to that motion, we don’t know what amendments are going to be selected for debate.

The PM confirmed she would be giving MPs an update on the Brexit talks tomorrow, saying she would tell them: “We will be making clear we have been making progress, we have had positive and constructive discussions. When we next bring the meaningful vote, it’s important people focus on whether we want to deliver on the result of the referendum and do that in a smooth and orderly way by leaving with a deal.”

Stephen Barclay, the Brexit Secretary, and Geoffrey Cox, the Attorney General, will be back in Brussels tomorrow for more talks with EU officials.

The three Cabinet ministers wrote in a joint article at the weekend: "If there is no breakthrough in the coming week, the balance of opinion in Parliament is clear: that it would be better to seek to extend Article 50 and delay our date of departure rather than crash out of the European Union on March 29.”

They added: "It is time that many of our Conservative parliamentary colleagues in the ERG recognised that Parliament will stop a disastrous no-deal Brexit on March 29. If that happens, they will have no one to blame but themselves for delaying Brexit."

Responding to Mrs May’s latest remarks, Labour’s Jo Stevens for the pro-EU Best for Britain campaign said: “From the Prime Minister that brought us 'Brexit means Brexit', Maybot is now claiming that 'any delay is a delay'.

“While the tectonic plates are shifting on Brexit, the Prime Minister continues to have her fingers in her ears. It is shameful that May is holding the country to ransom by toying with a cliff-edge Brexit.”

She added: “It’s time for the Government to do the right thing and put the country first. The people want their voice back on Brexit.”