Both sides showed "flexibility and a commitment to bring the current Brexit uncertainty to a close", said a spokesman for May s Downing Street office.
Irish Prime Minister Leo Varadkar said he believed European Union leaders were open to further delay and German Chancellor Angela Merkel said she would "fight until the last minute" for an orderly British exit.
Junior Brexit Minister Christ Heaton-Harris said on Wednesday that he had also quit May's government.
After failing repeatedly to win Parliament's backing for her Brexit blueprint, Britain's Prime Minister Theresa May dramatically changed gear Tuesday, saying she would seek to delay Brexit _ again _ and hold talks with the opposition to seek a compromise.
At a summit last month, they said that, to secure a delay to Brexit beyond April 12, May must either get the Withdrawal Agreement passed by March 29 or present a new plan.
The House of Commons has also failed to find a majority for any alternative plan in two days of voting on multiple options.
"A "no-deal" at midnight on the 12th of April is now a very likely scenario", he told the European Parliament.
EU Economy Commissioner Pierre Moscovici said a "no-deal" Brexit would mean long lines at borders and paperwork headaches for customs checks on the 11,000 vehicles entering and leaving Britain each day.
The proposal for any Brexit deal to be put to public vote in a "confirmatory referendum" was backed by opposition parties, plus some of May's Conservatives. Labour wants the U.K.to remain in the EU's customs union - a trading area that sets common tariffs on imports to the bloc while allowing free trade in goods moving between member states.
Meanwhile, the move of May infuriated pro-Brexit Conservatives who say Britain has to make a clean break trade policy and so as to take control of its laws.
"If passed, this bill would place a severe constraint on the government s ability to negotiate an extension and reflect this new date in United Kingdom statute books before April 12".
"I think the result will nearly certainly be, if Corbyn gets his way, that we remain in the customs union so that we can't control our trade policy, that there are huge areas of lawmaking we can't control, and Brexit is becoming soft to the point of disintegration", Boris Johnson, May's former Foreign Secretary, said according to The NYT.
"'It now seems that you and your cabinet have decided that a deal - cooked up with a Marxist who has never once in his political life put British interests first - is better than 'no- deal", Nigel Adams said as he resigned as a minister for Wales.
He was followed by junior Brexit minister Chris Heaton-Harris, who said in his resignation letter that the government "should have honored the result of the 2016 referendum" and left the European Union on March 29.
May has conceded that Britain will need a further delay to its departure in order to sort out the mess and avert a "no-deal" departure.