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 EU member Ireland
British Prime Minister Theresa May on Sunday called for still more time to renegotiate her Brexit deal, and drew outrage by suggesting parliament may not be able to vote on the text until just 17 days before Britain leaves the EU.
Business leaders and MPs reacted with anger and dismay at the news, which also prompted fresh calls to delay Brexit to avoid a damaging "no deal" exit on March 29.
Three of May's ministers had earlier warned that the House of Commons would seek a delay if there was no breakthrough this week.
May had raised the possibility of a vote on her deal in the coming days, but said on Sunday she was still negotiating with the European Union.
"As we're continuing with those talks, we won't bring a meaningful vote to parliament this week," she said at a summit of European and Arab leaders in Egypt.
"But that will happen by March 12. And we still have it within our grasp to leave the European Union with a deal on March 29."
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 EU member Ireland.
She met with European Council chief Donald Tusk in Sharm el-Sheikh and will also hold talks at the summit with German Chancellor Angela Merkel, while her team will return to Brussels on Tuesday.
But Labour's Brexit spokesman Keir Starmer said her move was "the height of irresponsibility and an admission of failure."
"Theresa May is recklessly running down the clock in a desperate attempt to force MPs to choose between her deal and no deal," he said.
Business leaders also expressed dismay.
"This is the latest signal to businesses that no-deal is hurtling closer. It must be averted," said Josh Hardie, deputy director general of the CBI lobby group.
Adam Marshall of the British Chambers of Commerce added: "These endless political manoeuvres aren't helping the businesses, communities or people of the UK to prepare for the changes that lie ahead."
Calls to delay Brexit
May says she does not want Britain to leave the EU without a deal, which experts warn could cause major economic disruption on both sides of the Channel, but she argues this requires MPs to back her plan.
Growing numbers of lawmakers, however, believe that Brexit may need to be delayed.
Business minister Greg Clark, work and pensions minister Amber Rudd and justice minister David Gauke on Saturday warned that if there was no breakthrough this week, parliament would seek the delay option.
"Beyond the next few days, there simply will not be time to agree a deal and complete all the necessary legislation before March 29," they wrote in an article in the Daily Mail.
May will address the Commons on Tuesday. then on Wednesday MPs will have the chance to debate their own ideas for the way forward.
A member of May's Conservative Party, Nick Boles, urged fellow lawmakers to back a cross-party plan to delay Brexit on Wednesday.
"MPs need to insert some rigour into this process," he said.
After rejecting the withdrawal deal that May spent almost two years negotiating with Brussels, MPs voted by a slim majority to request she seek changes to the Irish backstop.
This arrangement would keep Britain in a customs union with the EU after Brexit if and until another way - for example, a free trade deal - were found to keep the border with Ireland free flowing.
The EU has said it will not reopen the text, but is looking at what "guarantees" could be given to reassure MPs that the backstop would be temporary.
But Tusk emphasised during his talks with May that the other 27 member states would not sign off on anything until they were confident the Commons supported it.
"Tusk recalled the need for EU27 to have clarity that a proposal for the way forward can command a majority in the UK, before the issue is tackled by the European Council," an EU source said.
Earlier, Environment Secretary Michael Gove said the government was still looking at a time limit or unilateral exit mechanism for the backstop as a way to assuage MPs' concerns.
Alternatively, "it could be another legally powerful protocol or addition to the treaty that makes it clear that we would not be bound in the backstop indefinitely against our will."