Boris Johnson is set to meet German Chancellor Angela Merkel in Berlin later, where he is expected to reiterate his call for the backstop plan to be scrapped.
The PM has said the arrangement to avoid a hard border in Northern Ireland is “anti-democratic” and must be removed to secure a Brexit deal.
But the EU has rejected the possibility of any changes to the backstop.
Mr Johnson said the EU’s response to his demands was “a bit negative”.
However he said he would enter Brexit talks with “a lot of oomph” and there was “a real sense that something needs to be done” with the backstop.
“We can’t get it through Parliament as it is,” he added.
Mr Johnson is also expected to tell Ms Merkel the EU should not make the mistake of believing Parliament could somehow block the UK from leaving on the 31 October deadline.
The prime minister will also reiterate that, while he wants a deal, if the EU is not willing to negotiate the UK will still be leaving at the end of October.
Speaking ahead of the meeting, Ms Merkel said a solution could be found to the Irish border issue that meant the backstop would not be needed – but indicated there would be no change to the withdrawal agreement.
Mr Johnson’s meeting with the German chancellor is the first in a series of talks with EU leaders.
On Thursday, Mr Johnson will travel to Paris to meet French President Emmanuel Macron and on Saturday he will attend the G7 summit alongside other world leaders including US President Donald Trump.
In a letter to European Council President Donald Tusk on Monday, Mr Johnson said the backstop – which is part of the withdrawal agreement negotiated by former prime minister Theresa May – risked undermining the Northern Irish peace process.
The deal has been rejected by Parliament three times and Mr Johnson argued it would not be passed by MPs unless the backstop was removed.
But one Conservative MP has said Mr Johnson is “hell-bent” on a no-deal Brexit and there was “no chance” of him negotiating a new deal with the EU.
Ed Vaizey, who wants to prevent a no-deal exit, told BBC Radio 4’s Today programme: “We’ve been looking at the wrong target. The EU has said again and again and again this is the deal. They’ve got 27 countries to support it; we can’t even get 350 MPs to support it.
“We’re going to keep coming back to the Withdrawal Agreement, we’re going to continue to have a hung Parliament and a zombie Parliament unless and until we leave the EU and parties can then campaign to try and get a majority.
“So we have to find a way to get Parliament to agree to a deal and therefore I would give Boris Johnson the credit of at least forcing on Parliament an existential crisis by being faced with a prime minister who is hell-bent on getting no-deal.
“He is completely serious about no-deal and there’s no chance of him negotiating a deal with the EU, he knows that, he’s just going though the motions.”
He added that the onus was now on “people like the Green Party, the Liberal Democrats and the Labour Party” who should support the withdrawal agreement if they genuinely want to avoid a no-deal Brexit.
The Irish border is a matter of great political, security and diplomatic sensitivity, and both the UK and EU agree that whatever happens after Brexit there should be no new physical checks or infrastructure at the frontier.
The backstop is a position of last resort to guarantee that, but if implemented, it would see Northern Ireland stay aligned to some rules of the EU single market.
It would also involve a temporary single customs territory, effectively keeping the whole of the UK in the EU customs union.
European Council President Donald Tusk said those opposing the backstop without “realistic alternatives” supported re-establishing a hard border.
The European Commission said Mr Johnson’s letter did not contain a “legally operational solution” to the Irish border issue.
UK officials ‘unshackled’
Meanwhile, the government has announced that British officials will stop attending most EU meetings from 1 September, only taking part in those where the UK has a “significant national interest”.
The Department for Exiting the European Union said it would “unshackle” them from discussions “about the future of the Union after the UK has left” and allow them to focus on “our immediate national priorities”.
But the SNP’s Fiona Hyslop expressed concern the move could leave Scotland and the UK unrepresented while it was still a member of the EU.
The government is also ramping up its preparations for no-deal, announcing it will automatically enrol UK firms in a customs system to enable them to continue trading with the EU after Brexit.
However, Labour called for ministers to “put businesses and the economy first, and rule out a no-deal Brexit”.
Shadow chief secretary to the Treasury Peter Dowd said the “panicked announcement” was “late in the day” for businesses and would “not come close to mitigating the disastrous effects a Tory no-deal Brexit will have on small business exporters”.