A dispute between the UK and France over post-Brexit fishing rights has escalated significantly after a meeting between Boris Johnson and Emmanuel Macron, with Downing Street rejecting a French claim that the two leaders had agreed a path towards resolving the issue.

Johnson and the French president met alone for half an hour on Sunday morning on the fringes of the G20 summit in Rome, where they discussed next week’s Cop26 climate summit, as well as tensions over Northern Ireland and fishing.

French officials said after the meeting that there had been agreement over a path towards de-escalating the fishing dispute, in which Paris has raised the threat of trade barriers over what it says is the unfair allocation of post-Brexit licences to fish in UK waters.

The two countries had agreed to work on “practical and operational measures” to resolve the dispute in the coming days, Macron’s officials said, adding: “We are giving ourselves the space for de-escalation in the coming hours.”

When asked about this, however, Johnson’s spokesperson denied that any agreement had been reached, or that there were even formal plans for more talks to discuss the situation.

“I’ve seen some of the same reporting following that meeting,” he said. “It will be for the French to decide whether they want to step away from the threats they have made in recent days about breaching the Brexit agreement. Of course, we would welcome that if they want to de-escalate the threats that they have made.”

Asked whether this meant no agreement had been reached, the spokesperson said: “You would have to ask the French government about whether they want to proceed with the threats they have made.”

Questioned about the comments by French officials that the leaders had agreed to more “exchanges” between the two sides, Johnson’s spokesperson said: “If the French government wishes to come forward with how they want to de-escalate the threats that they have made, then we would absolutely welcome them.

“The position we are in is that the French government has made a series of threats about what they will do, and they have imposed their own deadline. It is now up to the French government about whether they wish to resile from that position, but our stance has not changed.”

The conflicting briefings come a day before Johnson is due to formally open the Cop26 meeting in Glasgow, one the prime minister has repeatedly said is crucial to the future of humanity.

Downing Street officials declined to say why, in their view, the French had given a seemingly misleading account of the meeting, but they did raise the possibility that the “mooted” exchanges were simply a reference to more standard, lower-level contact between officials that would be expected anyway.

Johnson had sought to play down the dispute earlier at the G20 gathering, when he stressed his close links to Macron and said he had “bigger fish to fry” in terms of preparing for Cop26.

Johnson’s Brexit minister, David Frost, has been more outspoken, expressing alarm at French threats to impose barriers on trade, and potentially on energy supplies, from Tuesday if there is no progress on fishing licenses.

Downing Street has said that if such measures were taken it would view them as breaching the post-Brexit trade and cooperation agreement, and that the UK could formally begin a dispute under the terms of the deal.

Downing Street’s formal account of the Johnson-Macron meeting said the prime minister “reiterated his deep concern over the rhetoric emanating from the French government in recent days, including the suggestion by the French prime minister that the UK should be punished for leaving the EU. He expressed his hope that the French government would de-escalate this rhetoric and withdraw their threats.”