European Council President Donald Tusk has said he would ask EU heads of state and government to be open to granting Britain a long extension of Brexit talks if London needs time to rethink its strategy of leaving the European Union.
"I will appeal to the EU27 to be open to a long extension if the UK finds it necessary to rethink its Brexit strategy and build consensus around it," Mr Tusk said on Twitter.
EU leaders meet to discuss Brexit on 21-22 March.
Mr Tusk said he would ask for openness to this option in his consultations with leaders in the run-up to the summit.
British MPs have voted to seek a delay in Britain's exit from the European Union.
The vote on extending Article 50 comes after MPs defied the government and dramatically decided to rule out a no-deal withdrawal from the EU in scenes some Tory Brexiteers described as "chaotic".
After the defeat, Mrs May made it clear that she intends to put a third "meaningful vote" on her Brexit deal to the Commons within days.
With just over two weeks to go until Brexit, Mrs May is using the threat of a long delay to push Brexit supporters in her Conservative Party to finally back her deal.
Steve Baker, leading member of the European Research Group (ERG) of Tory MPs, branded the situation a "fiasco".
Mr Baker said the ERG could try to prevent the law being changed to alter the scheduled exit date from the EU.
He said: "As a matter of practice, unless the law is changed, we leave on March 29.
"There are some things that we could do to prevent the law going through in the time that is available."
After the 149-vote rejection of her Withdrawal Agreement on Tuesday, Mrs May suffered a second defeat in as many days when MPs backed the cross-party amendment rejecting a no-deal Brexit under any circumstances yesterday evening.
In a surprise move, the Commons voted 312 to 308 - a majority of four - in favour of the proposal tabled by former Conservative chairman Dame Caroline Spelman.
The vote was later confirmed by a more emphatic 321 votes to 278, overriding a government motion from Mrs May that would have rejected no-deal on the scheduled date of 29 March but left it on the table for other times.
Meanwhile, German MEP Elmar Brok, who is a member of the EU's Brexit Steering Committee, said most of the EU member states do not want the UK to delay a decision on Brexit beyond 23 May, when European parliament elections are due to be held.
Speaking on RTÉ’s Morning Ireland, Mr Brok said "London must talk to London" and come up with a cross party solution that is acceptable to the EU.
He said he finds it "incredible" that the main parties are not talking to each other and it was "not a good show for democracy".
Mr Brok said that he did not understand why no one in the House of Commons is coming together in the national interest and he had no trust anymore that British politicians talk seriously to each other.
This is a view that was broadly shared across EU member states who, he said, were very dissatisfied with the situation.
He said that the UK must decide what it wants and find a broad consensus for a Brexit plan, before an extension could be granted.
Mr Brok added that the easiest thing to do would be to withdraw Article 50, which is still possible.