Boris Johnson is in Paris for Brexit talks with Emmanuel Macron, 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 of 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 has said the backstop must be ditched if a no-deal exit from the EU is to be avoided.
If implemented, the backstop would see Northern Ireland staying aligned to some rules of the EU single market, should the UK and the EU not agree a trade deal after Brexit.
It would also see the UK stay in a single customs territory with the EU, and align with current and future EU rules on competition and state aid.
These arrangements would apply until both the EU and UK agreed they were no longer necessary. Brexit supporters fear this could leave the UK tied to the EU indefinitely.
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.
Mr Macron said he was “very much confident” that the UK and EU would be able to find a solution within 30 days – a timetable suggested by Mrs Merkel – “if there is a good will on both sides”.
Mrs Merkel has argued that the withdrawal agreement does not need to be reopened if a practical solution to the backstop can be found.
Earlier on Wednesday, an official in Mr Macron’s office said France now saw a no-deal Brexit as the most likely scenario.
The UK is due to leave the EU on 31 October, with no deal being the default option.
Mr Macron said he saw no reason to grant a further delay to Brexit unless there was a significant political change in the UK, such as an election or a new referendum.
French officials said if the UK requested an extension in order to hold a new election, the EU would probably grant it.
After meeting Mr Macron on Thursday, Mr Johnson will attend the G7 summit on Saturday alongside other leaders including US President Donald Trump.
Meanwhile, Labour Party leader Jeremy Corbyn has cancelled a trip to Ghana later this week, urging opposition MPs to meet to discuss ways to prevent a no-deal Brexit.
Mr Corbyn has proposed that in order to prevent a no-deal exit, opposition MPs should help him defeat the government in a no-confidence motion and install him as a caretaker PM.
If he wins the vote, he plans to delay Brexit, call a snap election and campaign for another referendum.
However the Liberal Democrats, and some potential Tory allies opposed to a no-deal exit, have indicated they will not back a plan that leads to Mr Corbyn in No 10.
The prime minister has said he wants to leave the EU with a deal, but that the UK would be ready for a no-deal Brexit.
The Cabinet Office has announced it will stop using non-disclosure agreements for organisations working with the government on Brexit unless strictly necessary. For three years such groups have had to sign legally binding contracts agreeing to maintain confidentiality.