On Sunday, the prime minister told MPs they would get their chance to have a final "meaningful vote" on her deal by 12 March – only 17 days ahead of Brexit – causing criticism from opposition MPs, fellow Tories and business leaders.
Mrs May has been at the EU-League of Arab States summit in Egypt for two days and held a number of meeting with EU leaders on the fringes as she presses for more concessions to her deal.
The major sticking point is the backstop – the policy to prevent a hard border returning to the island of Ireland.
Parliament voted for her to return to Brussels to seek "alternative arrangements" to replace it, as critics feared it would keep the UK locked into EU rules indefinitely.
Her team has been discussing proposals with EU officials, including introducing a time limit to the policy or creating a get-out clause for the UK.
But the EU has repeatedly refused to reopen the withdrawal agreement – the so-called "divorce bill" element of the deal that includes the backstop.
Mrs May said: "There is still more work to do, and my team will be in Brussels [on Tuesday] working on the legally binding assurances that the UK Parliament needs in relation to the backstop.
"But 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."