Meanwhile, Downing Street said in a statement that May had sought to reassure French President Emmanuel Macron that the United Kingdom government was "working very hard to avoid the need for the U.K.to take part" in EU Parliamentary elections.
A Downing Street spokesman said: "Following the Prime Minister's letter to Donald Tusk last week, the leaders discussed the UK's request for an extension of Article 50 to June 30th, with the option to bring this forward if a deal is ratified earlier".
May wants to push back Brexit from 12 April to 30 June to arrange Britain's orderly departure but Brussels fears that will not be long enough, and European Union leaders are expected to offer a delay of up to a year.
The cross party talks in Westminster, looking to break the impasse that has so far blocked the House of Commons finding majority support for a Brexit deal, concluded Tuesday night.
German Chancellor Angela Merkel has warned Theresa May the European Union is likely to agree to a longer Brexit delay than the one she is asking for.
EU members want to ensure that a semi-detached Britain does not seek leverage in Brexit talks by intervening in choosing the next head of the European Commission or the next multi-year EU budget.
Three US soldiers killed in Afghanistan
The Taliban have held talks with a USA envoy in recent months while continuing to carry out daily attacks on Afghan forces. Abdullah said the Taliban could partake in elections and even compete for the presidency if they renounce violence.
And on Tuesday, US Treasury Secretary Steven Mnuchin warned American lawmakers: "I think at this point we need to be prepared for a hard Brexit as a very realistic outcome". The Prime Minister doesn't want to see a long extension.
The minister however sidestepped questions on BBC Radio 4 as to whether Mrs May could remain in office if a longer delay was pushed for by the EU.
He called for the European Council to discuss an alternative, longer extension, such as a "flexible extension" lasting "as long as necessary and no longer than one year".
Tusk, in a letter to the leaders of the remaining EU27, said there was "little reason to believe" that the ratification of Mrs May's beleaguered Brexit deal could be completed by the end of June.
Mr Tusk wrote: "The UK would be free to leave whenever it is ready". In reality, granting such an extension would increase the risk of a rolling series of short extensions and emergency summits, creating new cliff-edge dates.
The unanimous agreement of all 27 remaining European Union states is needed to avoid a no-deal Brexit on the scheduled date of April 12.
They will then meet for dinner without her to agree a response to the UK's extension request.