In the unlikely event that the Withdrawal Agreement passes, she has said that she will resign the leadership after the United Kingdom has left the European Union, which is due to take place on October 31.
Labour leader Jeremy Corbyn wrote to May on Friday, informing her that talks had "gone as far as they can" due to "the increasing weakness and instability" of the government.
May's Brexit deal has been rejected three times by parliament, and weeks of talks with the opposition Labour Party, the idea of which was deeply unpopular with many Conservatives, have failed to find a consensus on the way forward.
"Without significant changes, we will continue to oppose the government's deal as we do not believe it safeguards jobs, living standards and the manufacturing industry in Britain", Corbyn concluded.
The talks, which have lasted almost two months, were convened in an attempt to agree on a Brexit plan that could stand a chance of being approved by Britain's fractured Parliament. May will put part of her deal, contained in the Withdrawal Agreement Bill, to a vote in parliament in early June.
May shot back, attributing the lack of progress to Labour splits over a second referendum.
The pound sank to $US1.275 ($A1.855), its lowest level since mid-January.
The Labour leader has committed the party to retaining the "option" of a second vote, but only if the option of a Labour deal, or a general election, becomes impossible. Labour has feared any compromises on issues such as workers' rights would be torn up by Ms.
Cross-party talks in Britain aimed at striking a compromise Brexit deal have broken down without agreement.
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The large gathering is being planned for a grand welcome for Prime Minister Narendra Modi , said party leaders . You are fighting for the truth", Gandhi, head of the Congress party, said on Twitter .
The Prime Minister agreed to meet Sir Graham Brady, the chairman of the backbench 1922 Committee, at the start of June following a vote on the Withdrawal Agreement Bill to set the details of a leadership contest.
Before then, the government is considering holding a series of "indicative votes" to see what path, if any, lawmakers might be able to agree.
The prime minister had hoped to secure agreement with Labour to support, or abstain, on the crucial Brexit legislation required to take Britain out of the EU.
Britain was due to leave the European Union on March 29, but amid the political impasse in the country, the European Union extended the Brexit deadline until October 31.
"As we look to the future, we have to listen to the public", Simon Clarke, a Conservative lawmaker, said on Twitter.
The victor of a leadership contest will automatically become prime minister and will take control of the Brexit process, which has plunged Britain into its worst political crisis since World War Two.
That raises the prospect of a Conservative leadership battle producing a more Eurosceptic British leader who could move Britain towards a no-deal Brexit, the worst case scenario for sterling.
One source, writes the Daily Mail, said "Boris can not form a government, certainly not on a No Deal platform and probably not on any other".
Corbyn declaring the death of Brexit negotiations, which had entered their sixth week, cited May's decision to stand down as PM as a fundamental reason for the breakdown of talks, saying the government's authority has been "eroded".