Theresa May has written to the European Union to request a further delay to Brexit until 30 June.
The UK is currently due to leave the EU on 12 April and, as yet, no withdrawal deal has been approved by MPs.
The prime minister has proposed that if UK MPs approve a deal in time, the UK should be able to leave before European Parliamentary elections on 23 May.
But she said the UK would prepare to field candidates in those elections in case no agreement is reached.
It is up to the EU whether to grant an extension to Article 50, the legal process through which the UK is leaving the EU, after MPs repeatedly rejected the withdrawal agreement reached between the UK and the bloc.
The BBC's Europe editor Katya Adler has been told by a senior EU source that European Council President Donald Tusk will propose a 12-month "flexible" extension to Brexit, with the option of cutting it short, if the UK Parliament ratifies a deal.
But French President Emmanuel Macron's office said on Friday that it was "premature" to consider another delay while French diplomatic sources described Mr Tusk's suggestion as a "clumsy test balloon".
The prime minister wrote to Mr Tusk to request the extension ahead of an EU summit on 10 April, where EU leaders would have to unanimously agree on any plan to delay the UK's departure.
Mrs May has already requested an extension to the end of June but this was rejected at a summit last month.
Instead, she was offered a short delay to 12 April - the date by which the UK must say whether it intends to take part in the European Parliamentary elections - or until 22 May, if UK MPs had approved the withdrawal deal negotiated with the EU. They voted it down for a third time last week.
A Downing Street spokesman said there were "different circumstances now" and the prime minister "has been clear she is seeking a short extension".
Why 30 June?
The 30 June date is significant.
It's the day before the new European Parliament will hold its first session. So the logic is, that it would allow the UK a bit longer to seal a deal - but without the need for British MEPs to take their seats in a parliament that the UK electorate had voted to leave as long ago as 2016.
But, this being Theresa May, it's a plan she has previously proposed - and which has already been rejected.
It's likely the EU will reject it again and offer a longer extension, with the ability to leave earlier if Parliament agrees a deal.
But by asking for a relatively short extension - even if she is unsuccessful - the prime minister will be hoping to escape the ire of some of her Brexit-supporting backbenchers who are champing at the bit to leave.
And she will try to signal to Leave-supporting voters that her choice is to get out of the EU as soon as is practicable - and that a longer extension will be something that is forced upon her, rather than something which she embraces.
In her letter, the prime minister says she would continue to seek the "rapid approval" of the withdrawal agreement and a "shared vision" for the future relationship between the UK and EU.
She said if cross-party talks with the Labour Party could not establish "a single unified approach" in the UK Parliament - MPs would be asked to vote on a series of Brexit options instead which the government "stands ready to abide by", if Labour commits to doing the same.
The UK proposes an extension to the process until 30 June, she wrote, and "accepts the European Council's view that if the United Kingdom were still a member state of the European Union on 23 May 2019, it would be under a legal obligation to hold the elections".
To this end, she says the UK is "undertaking the lawful and responsible preparations for this contingency".
But it said if a withdrawal agreement could be ratified by Parliament before then "the government proposes that the period should be terminated early" so the UK can leave the EU before then, and cancel preparations for the European Parliamentary elections.