Starting today, leaders and government heads of 28 European countries and 21 Arab states will be convening a two-day summit in Sharm el-Sheikh to discuss joint challenges and boost mutual cooperation opportunities.
Speaking to reporters before travelling to an EU-Arab League summit in Egypt, May said on Sunday her Brexit negotiation team would continue talks with European Union officials in a bid to secure a deal palatable to British legislators, ruling out a vote this week.
The move has the potential to further sow discord within her Cabinet.
EU sources said the first EU-Arab summit is all the more important as the United States "disengages" from the region while Russian Federation and China make inroads.
Mr Clark, the business secretary, along with Ms Rudd, the work and pensions secretary, and the justice secretary, Mr Gauke, had earlier said they would be prepared to defy Mrs May and vote for a delay to Brexit.
"I was in Brussels last week", she said on a flight to Egypt for a summit in Sharm el Sheik. "While [I] do not want to see a no-deal scenario, the risk of failing to deliver on Brexit itself is too great to be contemplated".
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The latest delay comes after her Brexit plan was resoundingly defeated last month by 230 MPs - the biggest parliamentary defeat in British history - and underlines the difficulty May is having in attempting to get the agreement ratified.
On Wednesday, the Commons is expected to consider an amendment tabled by Labour MP Yvette Cooper and Conservative former minister Sir Oliver Letwin enabling the House to extend the Article 50 withdrawal process if there is no deal by mid-March.
On her way to Egypt where she hopes to get the approval of European Union leaders for her approach, May said further meetings in Brussels on securing changes to the deal ruled out a so-called meaningful vote this week.
'We are not a party of purges and retribution, ' Mrs May said at the NNC.
"Parliament can not stand by and allow this happen", Labour's Brexit Secretary Kier Starmer said in a tweet.
Three Cabinet ministers - Amber Rudd, David Gauke and Greg Clark - wrote a joint article on Saturday warning they can not allow the United Kingdom leave without a deal and suggesting they will vote to stop it on Wednesday.
"But I have been clear that we needed to, up to this point, keep no deal on the table and that is the default position". "The summit was always going to be more about symbolism than about any concrete decisions that might come out of it", Anthony Dworkin wrote in a commentary for the European Council on Foreign Relations think tank.