"The EU will want to know what use we mean to make of such an extension", May said.
This overruled the government's "no-deal" option that would only apply to the 29 March deadline and did not rule out the prospect of a no-deal exit later this year if Parliament is ultimately unable to agree a way forward.
May's Brexit deal, arrived at in November 2018, was first rejected by an enormous margin in January following a delay on the vote - the biggest defeat of any government in any vote, ever.
The DUP - which twice rejected Mrs May's deal in the Commons - said it was due to have talks with the government on Thursday to see if a solution could be found allowing its MPs to support the PM in a future vote.
Lawmakers voted by 391 to 242 against the deal, the second time they have defeated it.
If lawmakers reject a no-deal exit on Wednesday, another vote would then be held on Thursday on whether Britain should request from the European Union a limited extension of the March 29 Brexit date.
The EU, on its part, urged the UK Parliament to approve the deal brokered by May, reminding the MPs that simply voting against the no-deal scenario was not enough to untangle the Brexit mess.
Amendment A, which narrowly passed with 312 votes in favor and 308 against, rejects the United Kingdom leaving the European Union without a Withdrawal Agreement and a Framework for the Future Relationship.
Bolton: Some time may pass before a third Trump-Kim summit
But in the Vietnamese capital of Hanoi , the US side back-pedalled and called for a comprehensive deal, Moon said. Raddatz asked Bolton Sunday on "This Week".
For the Conservative Party parliamentarians, that vote will not go along party lines, May said.
Confirming that MPs will vote on Thursday on whether to ask her to request an extension of the Article 50 negotiation process, Mrs May said that they were facing a "fundamental choice". "The onus is now on every one of us in this House to find out what that is".
But Barnier also questioned the point of an extension at all, while addressing the European Parliament in Strasbourg, and warned that the risk of a no deal "has never been higher".
"Therefore the House has to understand and accept that if it is not able to support a deal in the coming days and if it is not willing to support leaving without a deal on the 29th of March then it is suggesting that there will need to be a much longer extension to Article 50".
In the staunchly pro-Brexit port of Dover in southern England, retiree Mary Simpson said she felt that her voice as a "leave" voter had not been heard. It's basically a buyers' market and all they are waiting for is some concrete information that we're headed for some kind of deal or second referendum and the pound is going to take off from there.
"We will be putting an amendment down to ensure Parliament considers an extension, it doesn't necessarily have to be a long extension", Labour's finance spokesman John McDonnell told Sky News. According to Barnier, the European Union "has done everything it can to get the withdrawal agreement over the threshold". The discussion on Article 50 is done and dusted.
Theresa May's deal covers such things as citizens' rights, the status of the Irish border and Britain's divorce bill from the EU.
Publishing "temporary" tariffs and arrangements in Northern Ireland for a no deal Brexit, the British government signaled that they want to keep the option on the agenda but it is likely that MPs will reject it Wednesday evening.