Jeremy Corbyn has tabled a motion of no confidence in Theresa May, after she said MPs would not vote on her Brexit deal until the week of 14 January.
The PM had delayed the vote from last week, admitting she was set to lose.
Labour leader Mr Corbyn said on Monday it was unacceptable for MPs to wait a month to vote, adding the PM had led the UK into a “national crisis”.
But No 10 sources told the BBC the government would not make time for the no-confidence vote.
Ministers would not “go along with silly political games”, they added.
Mr Corbyn tabled the motion calling on MPs to declare they have “no confidence in the prime minister due to her failure to allow the House of Commons to have a meaningful vote straightaway” on the Brexit deal.
The motion focuses on Mrs May personally, rather than the government.
BBC political editor Laura Kuenssberg said the motion could have been embarrassing for Mrs May, but as things stood, ministers would not allow time for it to be debated.
She said No 10 had effectively “batted the ball back to Labour to see if they have the guts” to call for a vote of no confidence in the government as a whole.
Unlike a vote targeting the PM, a motion of no confidence in the government could bring about an early general election if it is supported by a majority of MPs.
The SNP, the Lib Dems, Plaid Cymru and the Greens have tried to force Labour to bring about that situation, by trying to amend Mr Corbyn’s motion.
But Mr Corbyn said his aim in tabling the motion was to put pressure on her to have a vote on her Brexit deal this week.
Mrs May’s Brexit deal sets out the terms of Britain’s exit from the EU – on 29 March 2019 – and includes a declaration on the outline of the future relations between the UK and the EU.
But the deal only comes into force if both parliaments approve it.
Mrs May told MPs they would have the chance to vote on the deal she negotiated with Brussels in the third week of January.
Mr Corbyn said by then a month would have been wasted since the original 11 December vote was postponed, with “not a single word renegotiated and not a single reassurance given”.
“The deal is unchanged and is not going to change,” he said.
“The House must get on with the vote and move on to consider the realistic alternatives.”
However, Mr Corbyn came under fire from other opposition parties for limiting his no-confidence motion to the prime minister.
SNP leader Nicola Sturgeon tweeted: “Labour tabling a motion just in the PM rather than in the entire government begs the question, which Tory do they want to see as PM?”
And Nigel Dodds, of Northern Ireland’s DUP, which has propped up the Conservative government since June 2017, said: “We are not interested in the parliamentary antics or play-acting of the Labour Party.”
But Mr Corbyn told reporters late on Monday: “We haven’t failed to trigger any process. It’s this government that is denying Parliament the right to vote on this process, that’s why I tabled the motion.”
In other Brexit-related news:
- The SNP’s Westminster leader Ian Blackford was granted an emergency debate on Brexit for Tuesday, having said Parliament needed to “take control of the situation and find a solution”
- Theresa May rejected reports she was taking advice from predecessor David Cameron on what to do in the event of a Brexit deadlock in Parliament
- More than 60 MPs from various parties wrote to the PM urging her to rule out a no-deal Brexit, saying it would do “unnecessary economic damage” to manufacturers
- Irish foreign affairs minister Simon Coveney said Brexit might have to be delayed if the UK submitted an “entirely new” withdrawal proposal
In a Commons statement, Mrs May said MPs would resume the debate – halted last week – in the week of 7 January. The “meaningful” vote is due to take place the following week.
Mrs May told MPs: “It is now only just over 14 weeks until the UK leaves the EU and I know many members of this House are concerned that we need to take a decision soon.”
She said she had won fresh guarantees at last week’s EU summit over measures to avoid a hard border on the island of Ireland and she hoped to secure additional “political and legal assurances” in the coming weeks.
Earlier on Monday, an EU spokesman said it had provided the “clarifications” requested on the contentious issue of the Northern Ireland border backstop and “no further meetings were foreseen”.
During her statement, Mrs May faced calls from across the House for the vote to be held immediately.
Former education secretary Justine Greening said Mrs May had led the UK down a “political cul-de-sac”, adding: “She now isn’t just not listening, she is not allowing debate.”
Former cabinet ministers Dominic Raab and Esther McVey urged the PM to accelerate planning for a no-deal exit while another former minister, Andrew Mitchell, urged her to consider suspending the Brexit process to allow for further negotiations.
But Mrs May won support from one “previously sceptical” Brexiteer, Sir Edward Leigh, who said her efforts to secure a legally-binding protocol on the Irish backstop might pay off, urging her to “keep calm and carry on”.
Earlier, No 10 said it had “no plans” for votes on other Brexit outcomes if the PM’s deal is rejected after it emerged David Cameron had given advice to his successor.
The BBC understands Mr Cameron has been in touch with Mrs May about how a series of “indicative votes” on various different Brexit outcomes could be handled if there was deadlock over the terms of the UK’s exit.
Potential “Plan B” options include:
- pursuing different Norway or Canada-style arrangements with the EU
- leaving on the basis of a “managed no deal”
- delaying Brexit to restart negotiations
- hold a fresh referendum
The PM is coming under pressure from ministers to “test the will of Parliament” through a series of non-binding votes – which would see MPs pass judgement on the options available in the hope of identifying the most popular.
Business Secretary Greg Clark said he backed Mrs May’s deal but if Parliament was implacably opposed, it should be “invited to say what it would agree with”.