Video report by ITV News Political Correspondent Libby Wiener
Angela Merkel has told Boris Johnson a solution to the Northern Irish backstop could be found in the "next 30 days" after the PM demanded it be removed from the Brexit Withdrawal Agreement.
Mr Johnson said the "onus is on us" to produce solutions for the Northern Irish border and he welcomed a "blistering timetable of 30 days" to come up with the answers.
On his first foreign trip as Prime Minister, Mr Johnson said there was "ample scope" to achieve a deal with the EU but only if it dropped the backstop - the contingency plan aimed at preventing a hard border between the UK and Ireland.
Mrs Merkel said the backstop has always been a "fallback position" and would only come into effect if no other solution could be agreed that would protect the "integrity of the single market".
At a press conference ahead of a working dinner, she added: "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."
The German Chancellor said she wanted a Brexit outcome which allowed the UK and EU to continue to have "very close relations" - but acknowledged that the bloc had to be ready for the possibility of Britain crashing out without a deal.
Mr Johnson, who has repeatedly made clear the UK will also be ready to leave without a deal, said the only way to achieve one was to "remove" the backstop.
He said: "I think what we need to do is remove it whole and entire - the backstop - and then work, as Chancellor Merkel says, on the alternative arrangements.
"There are abundant solutions which are proffered, which have already been discussed. I don't think, to be fair, they have so far been very actively proposed over the last three years by the British Government.
ITV News Political Correspondent Libby Wiener says that Ms Merkel offered Mr Johnson an olive branch over the backstop issue, the Prime Minister has come away from the meeting with more than he thought he would.
"You (Mrs Merkel) rightly say the onus is on us to produce those solutions, those ideas, to show how we can address the issue of the Northern Irish border and that is what we want to do.
"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.
"You have set a very blistering timetable of 30 days - if I understood you correctly, I am more than happy with that."
But Paris now views a no-deal Brexit as the most likely outcome, according to French diplomatic sources.
The demand to scrap the backstop "limits the possibility of reaching an agreement", the official said.
Earlier Brussels insisted Mr Johnson would not be able to undermine the EU’s unity by holding bilateral meetings with the German and French leaders.
European Commission spokeswoman Natasha Bertaud said: "The EU27 have had from the outset – and continue to have now – one single, united position on Brexit matters."
Despite opposition to removing the backstop, in an interview with ITV News Mr Johnson claimed there are "plenty of other creative solutions".
He said: "I’m going to go of course and see if I can explore those ideas with our friends in Germany and France and at the G7 – let’s see where we get to."
On those meetings, he said “It may be that for now, they stick with the mantra, rien ne va plus, and they can’t change a jot or a tittle of the Withdrawal Agreement.”
"Let's see how long they stick to that, I think there are plenty of other creative solutions."