Theresa May is preparing to make a fresh Brexit offer on the Irish border by Friday to try and break the logjam in negotiations amid warnings she may have to wait until the New Year for trade talks, the Irish prime minister has said.
With the clock ticking to the December 14 summit of the European Council which must decide whether sufficient progress has been made on the UK's divorce deal to clear the way for talks on the future relationship, there was no sign of a breakthrough on the crucial issue of the Irish border.
Irish Taoiseach Leo Varadkar's office characterised a phone-call with Mrs May as a "stock-taking" exercise, and later he made clear he would not back down on his position that Dublin's approval for the opening of the second phase of talks is dependent on agreement on the border.
But he said he discussed with the Prime Minister the idea of Britain amending its offer to win over the Northern Irish Democratic Unionist Party, which scuppered a proposed deal on Monday.
With Mrs May under intense pressure from business for certainty by Christmas over the transition to a new UK/EU relationship, Mr Varadkar said she is hoping to return with a new formal written offer "tonight and tomorrow".
The Irish PM said he would consider any new proposal, but added: "Ultimately it is up to them to come back to us, given the events that happened on Monday.
"And having consulted with people in London, she wants to come back to us with some text tonight and tomorrow."
After talks with Dutch PM Mark Rutte in Dublin, he said his "absolute red line" that Brexit should not create a hard Irish border remains.
And earlier he told the Irish Dail: "We want to move to phase two but if it is not possible to move to phase two next week because of the problems that have arisen, well then we can pick it up of course in the New Year."
Mr Rutte made clear the EU would not compromise and allow the Irish border to kicked down the road to phase two of the talks, even under threat of Britain crashing out with no deal or divorce negotiations dragging on to 2018.
"You cannot just say because we need a soft Brexit that we will somehow compromise on some of the fundamentals on the three issues now on the table - citizens' rights, the exit bill, the border," he said.
"On each of three issues these sufficient progress needs to be established and if somehow your scenario would play out and somewhere along the line Britain would opt for a hard Brexit all by itself, the impact on the United Kingdom would again be infinitely bigger than on us."
He added: "We will not loosen our position. We will stay very firm."
Downing Street said Mrs May told Mr Varadkar she was "working hard to find a specific solution to the unique circumstances in Northern Ireland" and was committed to "moving together to achieve a positive result on this".
The PM also spoke by phone with Democratic Unionist Party leader Arlene Foster, whose rejection of plans for "regulatory alignment" between Northern Ireland and the Republic led to the collapse of a proposed deal on Monday.
It is understood Mrs Foster has no immediate plans to fly to London for talks with Mrs May and any such move would depend on progress in talks.
A DUP spokesman said: "There is still plenty of work to be done.
"The (Government and DUP) teams in London are continuing to work through the detail".
Meanwhile, opposition MPs demanded that Brexit Secretary David Davis be sacked and face investigation for contempt of Parliament after admitting his department had produced no impact assessments of the likely effect of Brexit on different sectors of the UK economy.
And opponents of a hard Brexit accused the Government of being "breathtakingly dysfunctional" after Chancellor Philip Hammond revealed that - 18 months after the EU referendum - Cabinet has not yet discussed details of the UK's preferred long-term relationship with the EU.
Downing Street later said a discussion on the "end state" would be held in one of the two Cabinet meetings scheduled before the end of 2017.
But Liberal Democrat leader Sir Vince Cable questioned the long delay in taking this step, asking: "Is this because ministers know they will not be able to agree? Ministers are behaving like a couple no longer on speaking terms but forced to live under the same roof."
Mr Hammond also received a slapdown from Downing Street after suggesting it was "inconceivable" the UK would not pay a financial settlement to the EU, regardless of whether it obtains a trade deal.
The Prime Minister's official spokesman swiftly said the payment - estimated at up to £50 billion - was "dependent on us forging (a) deep and special future relationship with the EU".
At Prime Minister's Questions, Labour leader Jeremy Corbyn labelled the Government's Brexit approach a "shambles", with the DUP - on whose votes Mrs May relies for her Commons majority - "ruling the roost".
But Mrs May attempted to downplay the deadlock over the Irish border, insisting that it was an issue which could only properly be resolved in the context of the upcoming trade talks.
"We will deliver this," she responded. "We aim to deliver this as part of our overall trade deal between the United Kingdom and the European Union.
"And we can only talk about that when we get into phase two."