Boris Johnson has met Emmanuel Macron in Paris for Brexit talks, with the French president saying the UK’s vote to quit the EU must be respected.
But he added that the Ireland-Northern Ireland backstop plan was “indispensable” to preserving political stability and the single market.
The backstop, opposed by Mr Johnson, aims to prevent a hard border on the island of Ireland after Brexit.
Mr Johnson said that with “energy and creativity we can find a way forward”.
On Wednesday German Chancellor Angela Merkel said the onus was on the UK to find a workable plan.
UK Prime Minister Mr Johnson insists the backstop must be ditched if a no-deal exit from the EU on 31 October is to be avoided.
He argues that it could leave the UK tied to the EU indefinitely, contrary to the result of the 2016 referendum, in which 52% of voters opted to leave.
But the EU has repeatedly said the withdrawal deal negotiated by former PM Theresa May, which includes the backstop, cannot be renegotiated.
However, it has previously said it would be willing to “improve” the political declaration – the document that sets out the UK’s future relationship with the EU.