MPs may have to wait until 12 March for a meaningful vote on the government’s final Brexit deal, Theresa May has said in an intervention that will deepen splits in her cabinet.

The prime minister confirmed on Sunday that she would not hold the vote this week as she flew to Sharm el-Sheikh in Egypt, where she is due to discuss Brexit on the margins of an EU summit with Arab leaders.

It is a critical week for May, with many in the House of Commons having been expecting to vote on her deal.

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Without a reworked withdrawal agreement to bring back to MPs, she has promised to table an amendable motion, which will allow backbenchers another chance to try to block a no-deal Brexit.

May said: “My team will be back in Brussels on Tuesday. As a result of that, we won’t bring a meaningful vote to parliament this week, but we will ensure that that happens by 12 March. But it’s still within our grasp to leave the EU by the 29 March and that is what we are planning to do.”

Amber Rudd, the work and pensions secretary, is among three cabinet ministers who have publicly threatened to defy the prime minister by backing an effort to force the government to extend article 50 if no deal is agreed by mid-March.

Rudd published a public statement on Saturday with David Gauke, the justice secretary, and the business secretary, Greg Clark, warning about the risks of a no-deal Brexit.

May has imposed a 12 March deadline for a vote because it should be held before the chancellor’s spring statement on 13 March, Downing Street sources said.

May brushed off calls to change course. “What we see around the cabinet table are strong views on the issue of Europe. What we are doing as a government is ensuring we are doing everything we can to leave the Europe Union with a deal,” she said.

“People are talking about the extension of article 50 as if it solves the issue when of course it won’t. It defers the point of decision. There comes a point when we must make that decision.”

Asked what she would do if she lost the meaningful vote, she said: “Why is it that people are always trying to look for the next thing after the next thing after the next thing?

“It is pointless, we should focus on what we are doing now, which is working to get a deal and bring that deal to a meaningful vote, which I want to see passed by the House of Commons and leave on 29 March.”

Asked about the open defiance from the three cabinet ministers who have threatened to resign, she said: “I have recognised and others have recognised that there are strong views that are held on this issue. What we are collectively doing as a government and as a cabinet is working to get that deal.

“Parliament wants to see changes to the backstop. We have been working with the EU on that. Our focus is on leaving with a deal. My intention is to work with a deal.”

In a separate development, May pledged £200m to help victims of the war in Yemen as she arrived in Egypt. “We are playing our part and will continue to do so but there is still more that we as an international community can do,” she said.

“At the summit in Egypt, I will call on our partners in Europe and the region to continue to provide the aid that is so desperately needed.”

May is due to meet a Saudi delegation on Sunday and is expected to also raise the killing of the journalist Jamal Khashoggi.

Brexit will not be on the official agenda at the inaugural meeting of the EU-Arab League conference, but May is expected to hold meetings with the European council president, Donald Tusk, later on Sunday and Angela Merkel on Monday.