Mrs May also said that Cabinet collective responsibility had not broken down after pro-EU ministers signalled they could support backbench moves to delay withdrawal in order to prevent a no-deal exit from the bloc.
In a statement on his arrival in Sharm El Sheikh leading the UAE delegation to the summit, Sheikh Hamad highlighted the strategic economic relations between UAE and Egypt's which are based on mutual respect, common interest and a quest to establish peace, security, stability and development in the region.
Lawmakers last month rejected her withdrawal deal, and since then, May has sought to address their concerns about its so-called "backstop" plan for the border between Northern Ireland and European Union member Ireland.
The Egyptian president pointed out that the Arab countries and the European Union have historical ties of cooperation across the Mediterranean based in its strength on considerations of geographic proximity, cultural extension, mutual interests through decades, shared values and a honest desire for peace and stability.
"We must work together - countries of origin, transit and destination - in order to break the business model of smugglers and traffickers who lure people into unsafe journeys and feed modern-day slavery", said EU Council President Donald Tusk.
No 10 has played down the prospect of a breakthrough, and there is speculation that Mrs May will say she intends to come back to the House again in two weeks time when she addresses MPs on Tuesday.
The UK remains on course to leave the European Union on 29 March.
"Extension of Article 50 doesn't solve the problem".
British Prime Minister Theresa May held one-to-one talks with Tusk and was due to hold further bilateral meetings with European Union leaders as she tries to break the stalemate at home over her divorce agreement with the EU.
Last month, Mrs May's Brexit deal was rejected in the biggest Commons defeat for any administration in over a century, and last week, three Tories decided they could no longer stay in her party and defected to form a new group.
Emotions are running high across the United Kingdom following a historic vote in Parliament to reject Theresa May's proposed Brexit deal.
Meanwhile, senior Labour Party officials are reportedly moving closer to supporting a second Brexit referendum.
Speaking about the issue of illegal immigration from Arab countries to Europe, Sisi said this issue should be viewed as a way to cooperate.
Referring to Labour MP Peter Kyle's amendment, he said: "We're working with them to see can we have a re-draft of that amendment which people could vote for and I think there's a high possibility we could".
However Labour said the latest delay to the meaningful vote was "the height of irresponsibility and an admission of failure".