Theresa May says she does not have enough support to win a vote on her EU withdrawal deal “as things stand”.
She said she would continue trying to get MPs to back it before putting it to the Commons for a third time this week.
The PM will also order Tory MPs to vote against a bid by a group of MPs, headed by Tory Sir Oliver Letwin, to hold votes on alternatives to her plan.
The government would give MPs time to hold such votes, but Mrs May said she was “sceptical” about the process.
She said the government would not commit to delivering the outcome of the votes but would “engage constructively” with MPs.
“The votes could lead to an outcome that is un-negotiable with the EU,” she told MPs.
“No government could give a blank cheque to commit to an outcome without knowing what it is.”
DUP leader Arlene Foster told the prime minister her party had not changed its position and would not be backing the deal, in a telephone call after this morning’s cabinet meeting.
The prime minister said the “default outcome” remained leaving the EU without a deal.
“The alternative is to pursue a different form of Brexit or a second referendum,” she said.
“But the bottom line remains: if the House does not approve the withdrawal agreement this week and is not prepared to countenance leaving without a deal, we would have to seek a longer extension.”
That would mean holding European elections, she added, and would mean “we will not have been able to guarantee Brexit”.
She also confirmed that on Wednesday, the government will seek to change the UK’s 29 March departure date through a piece of secondary legislation, which will make 11pm on 12 April the earliest Brexit date.
But she warned MPs that even if they voted against the change, it would still happen because it was contained in a piece of international law.
Confirming that the government will oppose Sir Oliver Letwin’s amendment calling for indicative votes, Mrs May said it would set an “unwelcome precedent which would overturn the balance of our democratic institutions”.
She said the government would provide time for MPs to debate alternatives but added: “When we have tried this kind of thing in the past, it has produced contradictory outcomes or no outcome at all.”
Labour leader Jeremy Corbyn confirmed that his party will back Sir Oliver Letwin’s attempt to secure “indicative votes” on Brexit, telling MPs: “It is time for Parliament to take control.”
She has said she would only bring it back for a third Commons vote if there was “sufficient support” for it – and she spent the weekend trying to persuade Brexiteer Tories to get behind it.
But many are thought likely to take their lead from the DUP, which has led objections to the Irish backstop clause.
Meanwhile, the EU has said all its preparation for an “increasingly likely” no-deal scenario on 12 April has been completed.
Media captionTheresa May says she had expressed her “frustration with our collective failure to take a decision” over Brexit.
Jeremy Corbyn met the prime minister for over an hour earlier, and had what Labour described as a “frank and comprehensive exchange of views” on Brexit.
Mr Corbyn told the PM there was no basis for holding a third vote on her deal.