Video report by ITV News Political Correspondent Daniel Hewitt
Theresa May is facing resistance over her request to the EU for Brexit to be delayed potentially until June 30, with Brussels expected to insist on a longer extension.
The PM wrote to European Council president Donald Tusk requesting the delay, with an option to leave earlier if she can get a Brexit deal through Parliament.
In a three-page letter addressed to Tusk, the prime minister cited the House of Commons' inability to find a majority for a Brexit deal that would see Britain leave the EU in an "orderly fashion".
She added Parliament does not want to leave without a deal and the "government agrees that leaving with a deal is the best outcome".
If approved, this would be the second delay to Britain's departure from the European Union, which was due on March 29 this year.
Meanwhile, talks between Labour and the Conservatives aimed at finding a Brexit consensus appear to have so far failed.
A Labour Party spokesman said: "We are disappointed that the government has not offered real change or compromise."
Shadow Brexit secretary Sir Keir Starmer said the Government was "not countenancing any changes" to the wording of the Political Declaration setting out the framework for the future UK-EU relationship.
In a sign that talks with ministers have so far failed to produce a breakthrough, he said: "So far, the Government isn't proposing any changes to the deal. In particular it's not countenancing any changes to the actual wording of the political declaration.
"Now obviously that's disappointing; compromise requires change. We want the talks to continue and we've written in those terms to the Government, but we do need change if we're going to compromise."
If those talks have indeed failed to bring about any agreement, it will make the need for a longer extension much more likely.
The request will be considered at an emergency EU summit on April 10, where it requires the unanimous agreement of the leaders of the remaining 27 member states.
EU sources said Mr Tusk is recommending a longer postponement of one year, with a break clause in the case of earlier ratification, in a so-called "flextension" deal.
ITV News Political Correspondent Daniel Hewitt says it's interesting that Mrs May sent the letter on Friday because "she had a bit more time".
He said: "There's some suggestion she's done that for two reasons; one is to put pressure on Jeremy Corbyn to agree to some kind of deal before the EU meet next Wednesday.
He added: "Secondly Theresa May is trying to appease those Brexiters in her Cabinet who do not want a long delay."
The European Union has already agreed to an extension of Article 50, which would have seen Britain leave the EU on May 22 had MPs voted in favour of May's Withdrawal agreement.
Mrs May said she will look to get her Withdrawal Agreement approved before the European Parliament elections on May 23, but that "responsible preparations" will be made if her deal is rejected.
By asking the EU for another extension, Mrs May is seeking to avoid a no-deal Brexit which would see Britain leave on April 12.
In response to Mrs May's decision to request an extension, the DUP, whose 10 MPs prop up the government, said it was "unsurprising but unsatisfactory".
The statement went on: "The United Kingdom fighting European elections almost three years after a clear majority voted to leave the EU sums up the disorganised and slapdash approach taken to negotiations by the prime minister."
It added: "The prime minister should not waste any extension subcontracting the UK's future to Jeremy Corbyn."
Irish premier Leo Varadkar said nobody wanted a no-deal next week, but he reiterated that a situation of rolling cliff-edges was not favourable either.
MPs have already voted down her deal three times but she is holding talks with Jeremy Corbyn in the hope of gaining cross-party support to push it through.
In her letter, she wrote: "I am writing therefore to inform the European Council that the United Kingdom is seeking a further extension to the period provided under Article 50(3) of the Treaty on European Union, including as applied by Article 106a of the Euratom Treaty.
"The United Kingdom proposes that this period should end on 30 June 2019. If the parties are able to ratify before this date, the Government proposes that the period should be terminated early.
"The Government will want to agree a timetable for ratification that allows the United Kingdom to withdraw from the European Union before 23 May 2019 and therefore cancel the European Parliament elections, but will continue to make responsible preparations to hold the elections should this not prove possible."
Tusk is expected to put the options to EU leaders at a crunch-summit next Wednesday in a bid to prevent the UK leaving the bloc on April 12, the BBC reported.
The request comes amid continuing top-level talks aimed at finding a way out of the Brexit deadlock between the Government and Labour on Friday.
The discussions are taking place as Mrs May faces a week of hectic diplomacy as she battles to keep her EU withdrawal agenda on track.
Labour opened nominations on Thursday for candidates to stand in the European elections.
But Foreign Secretary Jeremy Hunt said there was "zero appetite" for the UK to elect MEPs almost three years after voting to leave the EU.
Mrs May faced a continued challenge to her authority from Parliament as the House of Lords debated a Bill aimed at extending the Brexit process in a bid to avoid a no-deal scenario.
The remaining stages of the European Union Withdrawal (No.5) Bill will be considered by peers on Monday, threatening a new political headache for the PM if it is approved.
The bill, brought forward by backbenchers including Labour’s Yvette Cooper, allows Parliament to determine the length of any Brexit extension the Prime Minister should request at the EU summit on April 10.