A delay is possible if it is very short and only if the Parliament in the next few days supports the agreement.
In Britain, taxis have been organised to collect MPs as the Deputy Speaker Lindsay Hoyle voiced fears of violence, while the Ministry of Defence has made 3,500 troops ready as part of "Operation Redfold", in the event of a no-deal Brexit, the BBC reported.
May used her remarks at a second press conference to focus on rallying MPs back home to her deal, urging them to pass the legislation. May scrambling to try once more to get it approved.
European Council president Donald Tusk said that the response to Britain's request for an extension to the Article 50 withdrawal process was agreed "unanimously" by leaders of the other 27 member-states. If Parliament does not agree a deal next week, the EU Council will extend Article 50 until 12 April. Following six hours of talks after Mrs May left the room, diplomats said leaders were still wrangling over possibilities.
Germany's Angla Merkel said May could have an extension, ideally to around 23 May, but if the PM fails to secure backing for a deal in London, the European Union was braced for the worst.
As of this writing, more than one million people had signed the petition demanding that May's invocation of Article 50 of the European Union's Lisbon Treaty, which allows a country to formally withdraw from the EU, be revoked.
"April 12 is the key date in terms of the United Kingdom deciding whether to hold European parliament elections", EU Council president and summit host Donald Tusk said, announcing the arrangement.
Arriving for the European Council meeting at midday, French President Emmanuel Macron hinted that a third rejection of the Brexit deal would lead to a "no deal" scenario: "We have to be clear". May presented a new plan.
The EU is keen to prevent Britain remaining in the bloc during the elections, as legal advice has said any new parliament may be invalid if Britain doesn't stage a poll.
She added: "We will, despite these measures we have taken, work until the last day - I will say until the last hour - to ensure that this emergency planning doesn't come into effect. I sincerely hope that we can do that with a deal". May had originally planned for the U.K.to officially leave the E.U.by March 29, but Parliament has twice rejected her plan by wide margins in the past two months, most recently in a 242-391 vote on March 12.
"What the decision today underlines is the importance of the House of Commons passing a Brexit deal next week", she insisted.
The agreement gives Ms.
"It's now time for MPs to decide".
Even if the government whips up enough votes, the deal may not even be put before Parliament.
A debate on the deal has been scheduled for Monday but Downing Street said no date has yet been fixed for a vote. May has to get 75 MPs to switch their vote and back the deal. But far from reassuring them, many concluded that she herself had little faith in overturning two previous heavy defeats by lawmakers in London.
And, if her deal is thrown out again, should she seek to steer Parliament towards suggesting an alternative - binding her, potentially, to advocating a plan she'd spent years rejecting?
At Westminster, MPs on all sides voiced anger at the Prime Minister's statement on Tuesday night that blamed Parliament for the continuing Brexit deadlock.
In addition, organized labor, represented by the TUC, and business, represented by the CBI, sent an urgent letter to Theresa May calling her to avoid a hard Brexit.