EU leaders have been urged to show patience with Britain over its struggle to find majority support for a deal, the President of the European council Donald Tusk said in response to May's announcement.
"The important thing now is that in any extension that we get from the European Union, we have an absolute clarity that as soon as we've done the deal, we are able to bring that extension to an end", finance minister Philip Hammond told ITV.
Finance minister Philip Hammond said it was an "expectation" that Brussels would offer a longer extension, but London would want to curtail it as quickly as possible after passing a Brexit deal.
The bill will have to be approved by the House of Lords in order to become law.
A Downing Street spokesman said the meeting, which lasted an hour and 40 minutes, had been "constructive, with both sides showing flexibility and a commitment to bring the current Brexit uncertainty to a close".
May said late on Tuesday that she planned to ask Brussels for a further Brexit extension as she tries to avoid a no-deal outcome.
But some in the Labour Party have cast her gambit as a trap aimed at scaring her own lawmakers into backing the thrice-defeated deal, or as a way to extend responsibility for the difficulties of Brexit to the Labour Party.
May didn't indicate how long an extension she would seek in the EU, although she said she hoped Britain and the agreement could pass at time, by May 22 to prevent engaging in elections to the European Parliament.
The impasse has already delayed Brexit for at least two weeks beyond the planned departure date of March 29 to 2200 GMT on April 12.
Grassroots party members as well as a number of politicians have called for May to be replaced with some warning her actions will "destroy the Conservative Party".
In the most significant development of the day, May held talks at her office in the House of Commons with Corbyn and his senior aides.
During their talks on Wednesday, Corbyn reportedly told May that Labour want a customs union with the EU and access to its single market.
The House of Commons has also failed to find a majority for any alternative plan in two days of voting on multiple options.
Speaking after the meeting, Mr Corbyn said there had not been "as much change as [he] had expected" in the PM's position.
Economists and business leaders warn that a no-deal Brexit would cause huge disruption to trade and travel, with tariffs and customs checks causing gridlock at British ports and possible shortages of goods.
"She was clear that leaving with a deal remains the best solution to ensure that we deliver on what people in Wales and the rest of the United Kingdom voted for", she added.
The Daily Telegraph reported the Conservative Party headquarters has been flooded with angry messages fearing May's strategy will harm the Conservative's prospects in town and city local elections on May 2.
Many Labour legislators, meanwhile, are still determined to keep Britain inside the European Union by holding a second referendum on Brexit, and they view Corbyn's pursuit of a "soft Brexit" that keeps close European Union ties as a betrayal of that cherished goal.
The prime minister seems "genuinely willing to listen", Wales' first minister has said after Brexit talks in London.
Barnier said "we can still hope to avoid it" if London produced a breakthrough before an April 10 European Union summit.
European leaders will continue deciding how to respond to Brexit, with Ireland's prime minister, Leo Varadkar, hosting German Chancellor Angela Merkel in Dublin later.
"If that's what it takes to do what the elected House of Commons asked us to do, that is what we will do", she said.