Boris Johnson is set to meet German Chancellor Angela Merkel later, as the EU rebuffed his call to scrap the backstop in a bid to secure a Brexit deal.
The Prime Minister will head to Berlin after European Council chief Donald Tusk said the UK was "not proposing realistic alternatives" to the controversial border plan and was effectively supporting the return of a hard border in Ireland.
But Ms Merkel appeared to strike a softer tone than Mr Tusk, as she said the EU would consider "practical" solutions for the Irish border after Brexit, although a key ally of the Chancellor downplayed expectations of progress in Wednesday's talks.
The Prime Minister has called the arrangement “anti-democratic and inconsistent with the sovereignty of the UK”, pointing out that it has been rejected by the UK Parliament three times.
Instead he has called for talks on the border plan - which the EU argues is the only viable way to avoid a hard between Northern Ireland and the republic if talks break down - to be kicked into the next phase of Brexit negotiations.
He has has suggested replacing the backstop with "alternative arrangements".
But Mr Tusk described the PM’s letter as “misleading” and “inaccurate”.
The PM acknowledged on Tuesday night that the initial response to his demands had been "a bit negative", as he vowed to give the push to find a deal "a lot of oomph".
“I think there is a real sense now that something needs to be done with this backstop," he said.
"We can't get it through Parliament as it is. So I'm going to go at it... with a lot of oomph, as you'd expect, and I hope we'll be making some progress in the course of the next few weeks."
Mr Johnson’s pledge came as Ms Merkel said the EU was willing to consider "practical" solutions for the Irish border after Britain leaves the bloc.
But she again made clear that the withdrawal agreement thrashed out by Mr Johnson’s predecessor Theresa May will not be reopened as the UK heads for the EU exit on 31 October.
"As soon as we have a practical arrangement where we can abide by the Good Friday Agreement and also define the borders of the [EU's] single market, we won't need the backstop," the German leader said.
"That means we will, of course, think about practical solutions, and I always say that if you want to find these solutions, you can do so in a short period of time," she said.
"The European Union is ready to do this, but we don't need to open up the withdrawal agreement. It's a question of the future relationship."
Speaking ahead of the trip, Norbert Röttgen, an ally of Ms Merkel who heads the German parliament's foreign affairs committee, told The Guardian that Mr Johnson "would have been well advised against writing" his four-page letter setting out his Brexit stance.
“The British Prime Minister starts his letter by saying he is personally committed to finding an agreement, but there is no sign in the rest of the letter that this is actually the case,” he warned.
Mr Röttgen added: "Merkel is politically and emotionally well inclined towards the British, and her willingness to maintain friendly relations between the two countries will be on display on Wednesday. But the extent to which the Johnson government is prepared to humiliate itself for a trade deal with the USA has not gone unnoticed in Berlin."
The PM's Berlin visit comes ahead of a trip to Paris on Thursday, where Mr Johnson will hold talks with French President Emmanuel Macron.