Theresa May wants U.K. Parliament to vote again on Brexit deal in early June

British Prime Minister Theresa May will try again next month to secure Parliament's backing for a Brexit deal so that the U.K. can leave the European Union this summer, May's office said Tuesday.

Downing Street said May intends to ask lawmakers to vote on a withdrawal agreement bill starting the week of June 3.

Parliament has three times rejected the divorce deal May and the EU struck late last year. The U.K.'s departure from the EU, long set for March 29, has been delayed until Oct. 31 while Britain's politicians try to break the deadlock.

May's office said in a statement that if lawmakers passed the bill, the U.K. could still leave the EU "before the summer parliamentary recess," which is likely to start in late July.

But it is far from clear how the government plans to persuade a majority of lawmakers to back May's EU divorce terms, since few legislators on either side of the Brexit divide seem prepared to change their positions.

Approving the bill, which implements the terms of Britain's departure, does not remove the need for Parliament to separately ratify the thrice-rejected EU withdrawal deal.

The government calculates that if a majority of lawmakers can be persuaded to approve the Brexit terms bill, they will then back the deal as well.

Approval not guaranteed

But passage of either looks like a longshot. May's Conservative government has held weeks of talks with the opposition Labour Party in an attempt to reach a compromise on some of the major sticking points, but so far without signs of much progress.

The two sides do not agree on how close an economic relationship the U.K. should have with the EU after Brexit. Both May and Labour leader Jeremy Corbyn are under strong pressure from their party members not to make concessions to their rivals.

However, neither side wants to be the one to pull the plug on negotiations.

May and Corbyn met fortalks Tuesday. Downing Street said the meeting was "useful and constructive." Their representatives are set to continue the talks Wednesday.

"We don't think there is a deal there yet," Labour economy spokespersonJohn McDonnell said.