UK Prime Minister Theresa May has asked the EU to delay the Brexit date further to 30 June, admitting that the UK will have to hold European elections and is ready to do so if it has not ratified a Brexit deal by 23 May.
Earlier, European Commission President Jean-Claude Juncker reiterated the EU's position that Britain could get the Brexit deadline extended to May 22 if May could persuade MPs to approve her withdrawal agreement.
The opposition said the Government has failed to offer any compromises over Brexit following three days of talks.
However, Sir Keir said the government's approach had been "disappointing" and that it had refused to consider changes to the "actual wording" of the political declaration.
He observed: "The conversations with the Labour party are continuing - they were continuing last night, and we're expecting to exchange some more text with the Labour party today".
May began talks with Labour on a compromise deal earlier this week after a majority of lawmakers rejected her withdrawal agreement for a third time.
France also poses doubt to the extension by calling the request "premature", and urges "a clear plan" that would justify the second delay, a source in the French presidency also said Friday.
Other members of the government have spoken out against the plan to contest the elections, with Brexit Secretary Stephen Barclay telling the House of Commons: "To have European parliamentary elections three years after the country voted to leave would be damaging to our politics as a whole".
Worries about a chaotic British exit are especially acute in Ireland, the only European Union member that shares a land border with the UK Any customs checks or other obstacles along the now invisible frontier would hammer the Irish economy and could undermine Northern Ireland's peace process.
Meanwhile, a string of cabinet ministers signalled that Tories could be prepared to compromise on Labour's key demand of a customs union arrangement with the EU - an idea loathed by Brexiteers.
But she warned that "the longer this takes, the greater the risk of the United Kingdom never leaving at all".
A senior European Union official said Tusk was considering an extension offer of up to one year, with the possibility of leaving sooner.
On Thursday, German Chancellor Angela Merkel said she would do everything in her power to prevent a no-deal Brexit. The outcome of those talks is eagerly anticipated, although the two party leaders will need to come up with something before the EU's emergency summit next week and the current Brexit deadline of 12 April.
To get another short extension, May will need to "provide clarity" to the other 27 leaders at a summit on April 10 on how she plans to move forward.
Also on Friday, a poll result revealed by the Sky News said that a quarter of the British public would boycott European Parliament elections if they happen in Britain in May.