MPs will be asked to vote again on Brexit on Friday but only on part of the deal negotiated with the EU.
They will vote on the withdrawal agreement on the Irish "backstop", divorce bill and citizens' rights.
But it will not amount to a third "meaningful vote" on the deal, as it will not include a vote on the UK's future relationship with the EU.
Amid anger from MPs, Andrea Leadsom said it was "crucial" if the UK wanted to secure a Brexit delay until 22 May.
"If we don't agree the Withdrawal Agreement tomorrow then we will not, so that leaves in doubt the future for the arrangements with the European Council," she said.
BBC political editor Laura Kuenssberg said Theresa May was essentially asking MPs to turn it into a game of two halves - just voting on the first part of the deal which sorts out the UK's departure and leaving the longer term part for the next few weeks.
But it is still not certain it will get through - both Labour and the Democratic Unionist Party say they will vote against the withdrawal agreement on Friday.
Commons Speaker John Bercow said the government's "new" motion and complied with his ruling that he would not allow a third "meaningful vote" on "substantially the same" motion as MPs have already rejected by historic margins twice.
The PM's deal includes a withdrawal agreement - setting out how much money the UK must pay to the EU as a settlement, details of the transition period, and the backstop arrangements - and a political declaration on the way the future EU-UK relationship will work.
What could be the outcome?
If MPs approve the withdrawal agreement on Friday, they will have met the requirements laid down by the European Council if they are to push exit day back to 22 May.
But under current law, it would not be enough to ratify the deal because only one part would be approved.
The government would either have to pass part two of the deal - the political declaration on the future relationship - at a later date, or change the law so that it is not needed to ratify the treaty.
Last week the European Council agreed to postpone Brexit beyond the expected date of 29 March - offering an extension until 22 May, if MPs approved the withdrawal agreement by the end of this week.
If not, it offered a shorter delay until 12 April - the date by which the UK would have to indicate whether it would stand candidates in the 2019 European Parliament elections - allowing the UK time to get the deal through or to "indicate a way forward".
Commons Leader Mrs Leadsom told MPs on Friday that the European Council would only agree to extend Article 50 until 22 May if MPs approved the withdrawal agreement by 23:00 GMT on Friday.
"It's crucial therefore that we make every effort to give effect to the Council's decision and tomorrow's motion gives Parliament the opportunity to secure that extension," she said.
"I think we can all agree that we don't want to be in the situation of asking for another extension and facing the potential requirement of participating in European Parliament elections."