UK Prime Minister Boris Johnson has complained to European Commission president Ursula von der Leyen about French threats in the on-going row over fishing licenses.

"The prime minister also raised his concerns about the rhetoric from the French government in recent days over the issue," a Downing Street statement said after a meeting with Von der Leyen in Rome at the G20 summit.

"The prime minister stressed that the French threats are completely unjustified and do not appear to be compatible with the UK-EU Trade and Cooperation Agreement or wider international law," the statement said.

The UK could trigger the dispute mechanism put in place to deal with fisheries disputes in the Brexit deal. That could end up leading to demands for compensation.

French President Emmanuel Macron says it is the UK which is not upholding its side of the bargain by failing to grant extra fishing licenses.

He says the credibility of the UK is at stake - both on the fishing issue and another part of the Brexit deal, the Northern Ireland Protocol, which the UK wants changes to.

In Rome, Johnson and Macron exchanged a fist bump but did not appear to speak to one another as the leaders gathered for a group photo. They are due to have a brief meeting on Sunday morning.

Fishing dogged Brexit talks for years. The industry, although accounting for a relatively small amount of GDP for both countries, has a lot of political influence on both sides of the Channel.

As the dispute has rumbled along, French Prime Minister Jean Castex sent a letter earlier this week to the EU calling on the bloc to demonstrate there is "more damage to leaving the EU than to remaining there."

The issue also escalated this week when a British scallop dredger was escorted to a French port after French officials said it did not have the correct documentation.

Both sides have since threatened to take further action, but a French diplomatic source told Reuters Macron shared Johnson's aim of easing tensions.

"Brexit was a sovereign choice, we respect that. It's taken years to negotiate. The deal was signed, it must be applied now. When you sign a piece of paper, you must be true to it," Reuters quoted the source as saying.