On the eve of an emergency EU summit in Brussels, chief EU Brexit negotiator Michel Barnier said the bloc was ready to grand a delay, but that the duration "has got to be in line with the objective of any such extension".
The draft did stress the EU was ready to upgrade the political declaration setting out the blueprint of the new EU-UK deal after Brexit should London so wish.
"We remain completely committed to delivering on Brexit, with both sides working hard to agreeing a way forward, appreciating the urgency in order to avoid European elections".
The PM is hoping that her cross-party talks with Labour will convince European Union leaders to give her a short extension to Article 50 at a summit in Brussels in Wednesday, before Britain leaves the bloc with No Deal by default on Friday.
Such an extension would mean the United Kingdom having to take part in European parliamentary elections, which would be anathema to hardline Brexiteer Tories, and the country could be sidelined from budget decisions in Brussels.
At a tense meeting in Downing Street, Eurosceptic Cabinet ministers expressed their dismay over the links with Mr Corbyn and the prospect of a lengthy delay to Brexit.
Another condition for an extension would require the United Kingdom not to disrupt the EU's decision-making, which could see it sidelined from budget decisions in Brussels, BuzzFeed reported.
The Commons Leader made the call after a senior German official said the United Kingdom must take "substantial steps" to break the Brexit stand-off. Parliament has voted tonight against the damage & chaos that No Deal would cause for jobs, manufacturing, medicine supplies, policing & security.
Number 10 said ministers and their shadow counterparts will continue cross-party talks later, as they try to break the Brexit deadlock.
Labour leader Jeremy Corbyn says Theresa May won't compromise [Getty Images] Mr Corbyn added: "Talks have to mean a movement and so far there has been no change in those red lines".
The bill was amended by peers to state that nothing in it prevented the prime minister from "seeking or agreeing" an extension, provided it was not earlier than May 22.
If the other European Union member states reject the request to delay Brexit to 30 June, then Britain has two choices - either leave the bloc without a deal or cancel Brexit altogether.
In a letter to European Union leaders ahead of the summit, Tusk said that granting a flexible extension of a year, with the option of leaving earlier, would prevent the risk of a rolling series of short extensions and emergency summits and give Britain time to rethink its strategy.