The move places a deadline on cross-party talks with Labour, with Number 10 expressing a “determination” to bring them to an end.
The government will bring forward a key piece of Brexit legislation at the start of next month, Downing Street has said.
Number 10 said MPs will vote on the Withdrawal Agreement Bill, which enshrines the prime minister’s Brexit plan into UK law, in the week beginning 3 June.
The announcement came following what Downing Street said were “useful and constructive” talks between Prime Minister Theresa May and Labour leader Jeremy Corbyn.
It places an effective deadline on those cross-party discussions, which Mrs May sought in the wake of her Brexit deal being defeated three times by MPs.
Mrs May reached out to Mr Corbyn in a bid to find a compromise deal that could break the deadlock, but there has been no breakthrough so far.
“This evening the prime minister met the leader of the opposition in the House of Commons to make clear our determination to bring the talks to a conclusion and deliver on the referendum result to leave the EU,” a Downing Street spokesman said.
“We will therefore be bringing forward the Withdrawal Agreement Bill in the week beginning the 3rd June.
“It is imperative we do so then if the UK is to leave the EU before the summer parliamentary recess.”
A Labour Party spokeswoman said Mr Corbyn voiced his “concerns about the prime minister’s ability to deliver on any compromise agreement”.
She continued: “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.
“Jeremy Corbyn made clear the need for further movement from the government, including on entrenchment of any commitments.
“The prime minister’s team agreed to bring back documentation and further proposals tomorrow.”