Labour is pushing May to accept a much closer post-Brexit alliance with the EU that includes participation in a customs union.
He also signaled optimism about next Wednesday's European Union summit, saying most European Union states agreed on a need to delay Brexit.
"I haven't noticed any great change in the government's position so far", Labour leader Jeremy Corbyn said Saturday. In particular, it's not countenancing any changes to the actual wording of the Political Declaration.
"Now obviously that's disappointing; compromise requires change".
"The Government and the Opposition hope to meet again on Friday for further work to find a way forward to deliver on the referendum, mindful of the need to make progress ahead of the forthcoming European Council".
In an attempt to convince Labour to sign up to a deal, No 10 is offering to enshrine in law a plan that would hand parliament a say in future trade talks with the EU.
"It is a freaky approach from someone who made great play of wanting to find consensus - and has just wasted yet more time", the First Minister posted on Twitter. "At the moment there is focus on delivering Brexit, but if a long delay becomes a reality I believe the noises off about removing the prime minister will become a cacophony", he said.
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"The fact is that on Brexit there are areas where the two main parties agree: we both want to end free movement, we both want to leave with a good deal, and we both want to protect jobs", May said in comments released by her Downing Street office.
Prisons minister Rory Stewart insisted there was "quite a lot of life" left in talks with Labour.
"Many Tory MPs are absolutely furious and a lot of them are writing to (1922 Committee chairman) Graham Brady saying she's got to go". "Of course, we have to be prepared to discuss them... in a constructive fashion".
France's Europe minister Amelie de Montchalin warned yesterday that an extension would not be granted automatically.
Mr Tusk's call may not be welcomed by all European Union leaders, including French president Emmanuel Macron, who has previously claimed that unless there was "credible justification" for an extension, then one should not be granted.
Moreover, May would face pressure to step down from her fellow Conservative members of the UK parliament if Brexit delays force the United Kingdom to take part in the elections to the European Parliament, slated for next month, according to the media outlet.
Her letter reads like a long explanation of why Britain has been forced to seek yet another extension and points the finger of blame on British MPs who have not only rejected her withdrawal agreement but also failed to come up with a credible alternative.