MPs will vote later on whether to ask the EU for permission to delay Brexit beyond the 29 March departure date.
It comes after MPs voted on Wednesday evening to reject a no-deal Brexit under any circumstances.
Prime Minister Theresa May could also make a third attempt to get her EU withdrawal deal through Parliament in the next few days.
The EU said there were two ways the UK could leave - with or without a deal, adding it was ready for either outcome.
The UK government said there could be a short delay to Brexit - or a much longer one - depending on whether MPs backed the prime minister's existing withdrawal deal, which has been agreed with the EU, by 20 March.
If MPs approve Mrs May's deal before next week's EU summit in Brussels, then the extension will be until 30 June.
However, the PM warned that if the deal - which has twice been rejected by overwhelming majorities - is not approved, a longer extension will be needed, requiring the UK to take part in elections for the European Parliament in May.
"I do not think that would be the right outcome," said Mrs May. "But the House needs to face up to the consequences of the decisions it has taken."
In a night of high drama, the Commons first voted on an amendment to reject the UK exiting the EU without a deal by a margin of four.
Then, in another vote, they reinforced that decision by 321 to 278, a majority of 43.
That vote was on a motion that said the UK should not leave the EU without a deal specifically on 29 March, but with the option of a no-deal Brexit at any other time. It had originally been the government's motion.
The government had wanted to keep control of the Brexit process, and keep no-deal on the table, so they ordered Conservative MPs to vote against their own motion.
That tactic failed. Government ministers defied those orders and there were claims Mrs May had lost control of her party.
Thirteen government ministers - including Work and Pensions Secretary Amber Rudd, Business Secretary Greg Clark, Justice Secretary David Gauke and Scottish Secretary David Mundell - defied the government whips by abstaining in the vote.
Work and pensions minister Sarah Newton voted against the orders of the whips and has now resigned.
Mr Mundell said he backed the PM's deal and had always made clear his opposition to a no-deal Brexit.
However, Wednesday's no-deal vote is not binding - under current law the UK could still leave without a deal on 29 March, unless an extension is agreed with the EU.
In a crisis there can be opportunity.
This is now a crisis - the rules that traditionally have preserved governments are out of the window.
The prime minister has been defeated again. Her authority - if not all gone - is in shreds.
But for Number 10 there's an opportunity too, because MPs will soon be presented with a new choice - back the PM's deal, which has already been defeated twice, or accept the chance of a delay to Brexit.
This isn't the choice of a government that's in control. But the tactic is to make the best of chaos.