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. A 'wasted' month
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." Media captionJeremy Corbyn: May taking shambolic government to new level
Mrs May appeared to have the support of pro-Brexit backbench critics who last week failed in a bid to oust her as Tory leader.
One of them, Steve Baker, said: "Eurosceptic Conservatives are clear that we accept the democratic decision of our party to have confidence in Theresa May as PM. We will vote against Labour in any confidence motion."
Corbyn doesn't even like the EU because it mandates the privatisation of society. But a lot of Corbyn's fans come form the corruption of the welfare state the factt it no longer serves its egalitarian purpose but instead provides fun and games for the middling sorts. His fans got to avoid work and instead study journalism so that grandma doesn't get a stairlift, his fans steal from the public till and use that money to keep asylum seekers out of their hometown. Corbyn himself is an old social democrat leading a group of social liberals from the swamp held together by the often contradictory ways in which people define the word "left", the word "left" has become like the national flag it simply induces emotion and doublethink. You and everyone who stands against everything you believe in rallying around the same flag because the flag is about not seeing the world as it is or other people for what they are. In this way confusion chalk and cheese become one.
ChesneyChrist: Corbyn doesn't even like the EU because it mandates the privatisation of society. But a lot of Corbyn's fans come form the corruption of the welfare state the factt it no longer serves its egalitarian purpose but instead provides fun and games for the middling sorts. His fans got to avoid work and instead study journalism so that grandma doesn't get a stairlift, his fans steal from the public till and use that money to keep asylum seekers out of their hometown. Corbyn himself is an old social democrat leading a group of social liberals from the swamp held together by the often contradictory ways in which people define the word "left", the word "left" has become like the national flag it simply induces emotion and doublethink. You and everyone who stands against everything you believe in rallying around the same flag because the flag is about not seeing the world as it is or other people for what they are. In this way confusion chalk and cheese become one.
Harbal: I know it's not against the rules, but people wanting news will go to the appropriate place for it; surely a forum is a place for expressing yourself.
Report threads that break rules, are offensive, or contain fighting. Staff may not be aware of the forum abuse, and cannot do anything about it unless you tell us about it. click to report forum abuse »
If one of the comments is offensive, please report the comment instead (there is a link in each comment to report it).
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.
A 'wasted' month
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."
Media captionJeremy Corbyn: May taking shambolic government to new level
Mrs May appeared to have the support of pro-Brexit backbench critics who last week failed in a bid to oust her as Tory leader.
One of them, Steve Baker, said: "Eurosceptic Conservatives are clear that we accept the democratic decision of our party to have confidence in Theresa May as PM. We will vote against Labour in any confidence motion."