German Chancellor Angela Merkel has told British Prime Minister Boris Johnson he has 30 days to come up with an alternative solution to replace the backstop.
Mr Johnson called her timetable "blistering", but said he was "more than happy" with her proposal to speed-up the talks.
The Conservative Party leader arrived in Berlin to kick-start talks to find an alternative to the backstop section of the Withdrawal Agreement.
Mr Johnson, in a letter this week to European Council President Donald Tusk, said Britain would leave without a deal unless the "anti-democratic" backstop - voted down three times by MPs in Parliament - was removed from the Withdrawal Agreement.
The backstop would require Britain to obey some EU rules if no other way could be found to keep an invisible land border on the island of Ireland.
The Irish Government says this is crucial to maintaining peace on the island.
A Government spokesperson said the EU has always said that the backstop is an insurance, which would only come into effect in the absence of other agreed arrangements.
"We await seeing detailed proposals from the UK which, if agreed, would mean that the backstop would not have to come into force," the spokesperson said.
Mrs Merkel, in a statement in the Chancellery in Berlin, said the backstop had always been a "fallback position".
She reiterated that it would only come into effect if no other solution could be agreed that would protect the "integrity of the single market".
In an attempt to have a backstop solution in place before the 31 October Brexit deadline, the German leader said she wanted a new arrangement agreed within 30 days.
She said: "If one is able to solve this conundrum, if one finds this solution, we said we would probably find it in the next two years to come but we can also maybe find it in the next 30 days to come.
"Then we are one step further in the right direction and we have to obviously put our all into this."
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Ms Merkel said she wanted Britain to spell out what a solution to the border problem would look like.
"We will first listen to Britain's proposals. Our goal is to preserve the integrity of the single market," she said.
"And just as we managed to discuss and solve issues with imagination within the European Union, I believe that you can also find ways here and this will be the task."
Mr Johnson said he was "more than happy" with the timetable proposed by his German counterpart.
"I must say I am very glad listening to you tonight Angela to hear that at least the conversations that matter can now properly begin," he said.
"You have set a very blistering timetable of 30 days - if I understood you correctly, I am more than happy with that."
A Downing Street source said the Government was happy with the tone of Mrs Merkel's exchange.
UK Prime Minister @BorisJohnson says the UK wants a deal on #Brexit, but "we cannot accept the current withdrawal agreement" and "we do need that backstop removed". pic.twitter.com/y5e1BcfHGy
— RTÉ News (@rtenews) August 21, 2019
The British government was not briefed beforehand that Mrs Merkel would apply the "pressure" of a 30-day deadline.
However, Mr Johnson's team is hopeful it is an indication that European leaders are preparing to renegotiate - an outcome the EU has previously ruled out.
Mr Johnson told Mrs Merkel that the backstop would have to go as part of further discussions - or else Britain was prepared to leave without a deal.
He said the backstop would need to be removed "whole and entire" before a deal could be reached.
But Mr Johnson, on his first trip to Germany as British leader, said he was optimistic an agreement could be struck.
"What in my experience happens is that people find a way through and I think that if we approach this with sufficient patience and optimism, as I say, we can get this done and it is in the final furlong generally when the horses change places and the winning deal appears," he told the press.
Mr Johnson and Mrs Merkel are set to hold talks over dinner, with the Chancellor telling reporters "we need to get to work now".
Mr Johnson is due to travel to France tomorrow to meet French President Emmanuel Macron in Paris to hold similar discussions.
However, this evening Mr Macron has dismissed demands from Mr Johnson to renegotiate the UK's exit from the European Union, saying it was "not an option".
"Renegotiation of the terms currently proposed by the British is not an option that exists, and that has always been made clear by (EU) President Tusk," Mr Macron told reporters in Paris.
Additional reporting AFP
