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 the Commons for a third time this week.
The Prime Minister 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 will give MPs time to hold such votes, but Mrs May said she was "sceptical" about the process. As many as six other options, in addition to Mrs May's deal, could be put to votes to see which are most popular.
She said the government would not commit to delivering the outcome of the votes but would "engage constructively" with MPs.
However, Mrs May was understood to have suggested the government would not be bound by the so-called indicative votes being planned by MPs.
She also confirmed that 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.
She warned MPs that even if they rejected the change, it would still happen because it was contained in a piece of international law.
Mrs May's EU deal has been overwhelmingly rejected in the Commons twice.
On Sunday, two cabinet ministers touted as potential successors said they fully backed the Mrs May as senior figures dismissed talk of a "coup".
Meanwhile she summoned leading Brexiteer opponents of her deal - including Boris Johnson, Jacob Rees-Mogg and Iain Duncan Smith - to her country retreat Chequers to assess whether there was enough support for it to bring it back to the Commons this week.
She has said she would only bring it back for a third Commons vote if there was "sufficient support" for it.
There was little sign of an immediate breakthrough however, and many are thought likely to take their lead from the DUP which has led objections to the Irish backstop clause. DUP has said its position has not changed and it will not be backing the withdrawal agreement.
It follows a week in which Mrs May was forced to ask the EU for an extension to Article 50 and hundreds of thousands of people marched in central London calling for another EU referendum.
Reactions as Brexit standoff continues
The EU has said all its preparation for an "increasingly likely" no-deal scenario on 12 April has been completed.
It said such an eventuality would cause "significant disruption for citizens and businesses" and "significant delays" at borders.
"In such a scenario, the UK's relations with the EU would be governed by general international public law, including rules of the World Trade Organisation," a statement said.
Labour leader 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.
Conservative MP Sir Oliver Letwin said that once Mrs May knew what it would take to get a majority vote it would help her find "a way forward in principle".
However, International Trade Secretary Liam Fox said there had to be an agreed deal by 11 April otherwise the UK will have to take part in EU elections which "would unleash a torrent of pent up frustration from voters".
"I'm answerable to my voters not to the House of Commons," he said.
Boris Johnson has described some of the suggested options - including a Norway-style close relationship with the EU - as "catastrophic" in an article in the Daily Telegraph.
Accusing Mrs May of "bottling" Brexit, the former foreign secretary said the only argument for backing what he called her "rotten deal" was if every other option was worse.
Meanwhile, Foreign Office Minister Mark Field said he would support revoking Article 50 - the two year process for leaving the EU - if it became an option in the event Mrs May's deal was defeated and free votes granted for indicative votes.
Labour MP Wes Streeting said he believed there to be a "genuine desire" to find a way through the deadlock "but the prime minister has to set Parliament free".
And Labour MP Peter Kyle said "what the country really wants" is for "grown ups to get a grip on this and show a creative and a solid way out of the madness".
What's happening this week?
Monday: MPs will debate the Brexit next steps and a number of amendments - possible alternatives - to the government plan will be put to a vote. The most important of these is the indicative votes plan.
Tuesday: Theresa May could bring her withdrawal deal back for the so-called third meaningful vote. The government however says it won't do that unless it's sure it has enough support to win.
Wednesday: This is when indicative votes would be held - we don't know yet whether MPs will be free to vote how they want or be directed along party lines. The chances of any genuine cross-party consensus being achieved are not high.
Thursday: A second possible opportunity for a third meaningful vote. The prime minister may hope that Brexiteers will finally decide to throw their weight behind her deal because indicative votes have shown that otherwise the UK could be heading for the sort of softer Brexit they would hate.
Friday: This is still written into law as the day the UK leaves the EU, but the PM is attempting to change that through a piece of secondary legislation. If she succeeds, the earliest Brexit will happen is 11pm on 12 April.