The PM says she wants to meet Labour leader Jeremy Corbyn to agree a plan on the future relationship with the EU.
Mrs May said, if a "single, unified approach" could not be agreed with Mr Corbyn, then they would move to "a number of options for the future relationship we could put to the House in a series of votes to determine which course to pursue".
The statement followed seven hours of meetings with Cabinet ministers, and came a day after the House of Commons yet again rejected alternative plans for Brexit during indicative votes.
President Macron told reporters that the European Union "cannot be hostage to the political crisis in the UK", and the government must come forward with "credible" reasons for an extension.
If passed into law, the bill would require the PM to ask for an extension of Article 50 - which mandates the UK's exit from the European Union - beyond the current 12 April deadline.
He said: "We will meet the Prime Minister".
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The group behind the bill, which also includes former Tory chair Dame Caroline Spelman, Commons Brexit Committee chair Hilary Benn, former attorney general Dominic Grieve and Liberal Democrat Norman Lamb, aims to push it through all of its Commons stages on Thursday, and hopes the House of Lords would then grant its approval ahead of the emergency European Union summit on April 10.
The PM said: "This is a hard time for everyone".
"She needs to put forward a proposal, including saying how long an extension she thinks we need to sort things out".
Tory MP Sir Oliver Letwin, who supports Ms Cooper's bill, said: "This is a last-ditch attempt to prevent our country being exposed to the risks inherent in a no-deal exit". This is not the first time Cooper or her conspirators tried to stop a proper, no deal Brexit, with Cooper, Letwin, and former Conservative MP Nick Boles threatening a government shutdown by presenting amendments to a finance bill which meant to stop the Treasury spending money on no deal arrangements. "But it is definitely worth trying", he added.
Last month, the Prime Minister said: "Unless this House agrees to it, no deal will not happen".
EU chief negotiator Michel Barnier says that Britain's exit from the European Union without a deal "becomes day after day more likely" after the United Kingdom parliament again rejected alternatives to the government's unpopular divorce deal. "Not the fantasy Brexit that was sold to them in 2016", he said.