The UK and the European Union will give their negotiators more time to reach a compromise in the trade talks after they agreed “on the importance of finding an agreement”.

Boris Johnson and European Commission president Ursula von der Leyen spoke via video conference on Saturday to take stock of progress in the negotiations following the final scheduled round of talks between Brussels and the UK this week.

Following their conversation on Saturday, the pair have tasked their chief negotiators with working “intensively” to resolve the remaining differences in the post-Brexit trade talks.

Fishing rights, state aid and governance continue to be vexed issues between the two sides as they look to ratify a new trading relationship before the transition period ends on December 31.

UK negotiator Lord Frost tweeted following the leader’s statement to confirm that discussions with his EU counterpart Michel Barnier would “begin as soon as we can next week”.

The Prime Minister, who will face questions on the BBC’s Andrew Marr Show on Sunday, has repeatedly asserted that any agreement needs to be wrapped up before the EU Council meeting on October 15, a deadline that is only 11 days away.

But in the weekend’s joint statement between Downing Street and the European Commission, there was no mention of a target date for a resolution.

“The president of the European Commission, Ursula von der Leyen, and the UK Prime Minister, Boris Johnson, spoke today about the state of play in the negotiations on the future relationship between the UK and the EU,” said the joint statement.

“They agreed on the importance of finding an agreement, if at all possible, as a strong basis for a strategic EU-UK relationship in future.

“They endorsed the assessment of both chief negotiators that progress had been made in recent weeks but that significant gaps remained, notably but not only in the areas of fisheries, the level playing field, and governance.

“They instructed their chief negotiators to work intensively in order to try to bridge those gaps.

“They agreed to speak on a regular basis on this issue.”

The shared decision by Mr Johnson and Ms von der Leyen to intensify the talks could pave the way for what is dubbed “the tunnel”, where the negotiating teams enter a media and briefing-free blackout in a bid to work out compromises on the outstanding differences.

The Prime Minister has struck a positive tone about the prospects of securing a trade deal in recent days.

He told reporters on a construction site visit in west London on Saturday that there is a “good deal to be done” with the EU.

Cabinet Office minister Michael Gove, who is in charge of Britain’s Brexit preparations, stressed that while the UK is ready for a no-deal scenario, a deal would be best for an economy recently ravaged by the impact of coronavirus.

If the UK fails to strike a deal with its largest trading partner, it would fall back on World Trade Organisation terms, with tariffs and border checks introduced on some British exports into the bloc as a result.

Mr Gove, speaking at the Conservative Party’s virtual conference, said: “If we can secure a negotiated outcome and a free trade agreement, that would be hugely helpful for sectors of the economy.”

Foreign Secretary Dominic Raab took a tougher line in his conference speech, in comments that have been seen as an attempt to pacify anxious Tory MPs that the UK could be preparing to buckle in the negotiations in order to get a deal.

In his speech to party members at the conference, he said the “days of being held over a barrel by Brussels are long gone”, as he stressed any trade deal must be “fair”.