"Talks this evening between the Prime Minister and the Leader of the Opposition were both useful and constructive".
Ministers and the Labour frontbench are in their seventh week of talks in an attempt to reach consensus.
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", the spokesman said.
The UK voted to leave the European Union by 52% to 48% in a June 2016 referendum.
Peter Bone has said it is "absurd" for the Prime Minister to bring her Withdrawal Agreement Bill back to the Commons for a fourth time.
But it is far from clear how the government plans to persuade a majority of lawmakers to back May's European Union divorce terms, since few legislators on either side of the Brexit divide seem prepared to change their positions.
No date has been set for the summer recess, but Parliament usually rises near the end of July.
"We don't think there is a deal there yet", Labour economy spokesperson John McDonnell said.
"No leader can bind his or her successor so the deal would likely be at best temporary, at worst illusory", said the letter.
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The conversations with Labour had been "difficult", the spokesman said, but ministers were "determined to find a way through" the Brexit impasse.
Seeing his party as failing to deliver its core manifesto pledges and being potentially punished at the polls as a result, veteran MP Blunt took to British television to say the party had to reinvent itself as one of Brexit.
For the past six weeks, ministers and their Labour counterparts have been discussing how Parliament might accept the agreement May struck with the European Union (EU) a year ago.
Some 13 former ministers, together with the chairman of the backbench 1922 Committee, Sir Graham Brady, have written to the Prime Minister urging her not to concede Labour's key demand.
Signatories include potential leadership contenders Boris Johnson and Dominic Raab.
May and opposition leader Jeremy Corbyn sat down for talks again on Tuesday ahead of further discussions between the government and opposition on Wednesday.
While European Union elections have always been seen as a safe place for mid-term protest votes to take place by the political establishment in the United Kingdom, polling showing that the month-old Brexit Party is now beating the Conservatives in even general election polling has sent shockwaves through Westminster.
"We believe that a customs union-based deal with Labour will very likely lose the support of Conservative MPs, like us, who backed the Withdrawal Agreement in March (in many cases very reluctantly), and you be unlikely to gain as many Labour MPs to compensate", they said. Vara, who voted for remain in the 2016 referendum, said May's deal "leaves the United Kingdom in a half-way house with no time limit on when we will finally be a sovereign nation".