A government spokesperson said May will put forward a Withdrawal Agreement Bill, making Brexit law in the UK, in the week of June 3, before the summer parliamentary recess in July.
Lawmakers have already rejected May's Brexit deal with the European Union three times amid deep divides over when, how or even if the divorce will take place.
Brexit Secretary Stephen Barclay said on Wednesday that a fourth defeat would mean the "deal is dead in that form" and force parliamentarians to choose between a no-deal Brexit or canceling Britain's departure completely.
"If the House (of Commons) has not passed the Withdrawal Agreement Bill then there are growing voices in Europe, not least the French, who want to move on to other issues," he said.
May's spokesman refused to say whether she would resign if she loses the vote.
Talks with oppositionMay reached out to the opposition Labour party last month to overcome deadlock in Parliament after some members of her Conservative party rejected her Brexit plan.
In talks this week, May was seeking a "stable majority in Parliament that will ensure the safe passage of the Withdrawal Agreement Bill and the UK's swift exit from the EU," her spokesman said Tuesday.
Brexit had been due to take place on March 29, but the deadline has since been extended to October 31 to buy the government more time to come up with a plan nearly three years after British voters opted to leave the EU.
Labour wants the UK to remain in the EU customs union in any Brexit scenario. Many Conservative MPs have rejected Britain remaining in the customs union.
May's authority in questionA Labour party spokesperson said Corbyn had raised "concerns about the prime minister's ability to deliver on any compromise agreement."
"In particular he raised doubts over the credibility of government commitments, following statements by Conservative MPs and Cabinet ministers seeking to replace the prime minister," his spokesman said.
May has promised to resign as prime minister, should the Brexit deal she struck with the EU last year pass. However, she is under pressure from Brexiteers maneuvering against a compromise with Labour — with some Conservatives eyeing her position.
On Tuesday, 13 former Conservative Cabinet members as well as Graham Brady, chairman of the 1922 Committee of Conservative lawmakers, wrote to May urging her not to agree to Labour's demand for a post-Brexit customs union with the EU.
"You would have lost the loyal middle of the Conservative Party, split our party and with likely nothing to show for it," the letter said. "We urge you to think again."
Peter Bone, a Brexit-supporting Conservative MP, told the UK's Talk Radio on Wednesday that other pro-Brexit Conservative lawmakers "think it (May's Brexit deal) is dead."
"They will vote against it this time ... It seems absurd to bring it back. It is the same thing again, again and again."
cw/cmk (AFP, dpa, Reuters)
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