Prime Minister Boris Johnson has acknowledged "turbulence" in the UK's relationship with France as the row over fishing rights escalates.
After dozens of French boats were denied post-Brexit fishing licences for UK and Jersey waters, France threatened to block ports to British vessels.
But Mr Johnson told the BBC the things that united the UK and France were more important than their divisions.
The French president said the row was a test of the UK's global credibility.
France has said it will take "targeted measures" against the UK if the row over fishing licences is not resolved by Tuesday.
A Downing Street spokesman said the government was prepared to continue working with France to issue more licences, but if France proceeded with its threats the UK would "act in a calibrated manner".
Pressed on how the UK would respond to the threats as the G20 group of major economies met, the prime minister told the BBC: "We're going to get on and do the things that matter to both of us and make sure that we work together on tackling the big issues that face the world."
He said that "there's some turbulence in the relationship", referring to a letter seen by the BBC in which the French Prime Minister Jean Castex said the EU must demonstrate in this dispute that there was "more damage to leaving the EU than remaining there".
"If one of our partners decides to breach the Trade and Cooperation Agreement that we struck, that's a matter that we have to pursue," Mr Johnson said.
The UK government suggested on Friday that France's threatened measures - such as blocking ports to UK boats, increasing checks on UK goods, boats and trucks, and even cutting energy supplies - would be a breach of the post-Brexit trade deal with the EU.
The prime minister also suggested the UK was concerned France may be "already in breach" of the deal.
Mr Johnson raised his concerns with European Commission head Ursula von der Leyen over the "rhetoric from the French government" at a meeting at the G20 summit, the prime minister's office said.
In a statement, a spokesman added: "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."
Mr Macron and Mr Johnson are expected to have an informal meeting on the margins of the G20 summit in Rome on Sunday.
But asked if he felt the French behaviour was unacceptable, Mr Johnson told the BBC the priority for the UK and France was making progress on tackling climate change in talks at the G20 summit and at COP26 in Glasgow.
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Speaking from the Colosseum in Rome, he invoked the collapse of the Roman Empire as he said the world was "absolutely conniving in our decline and fall".
"What we want to do is to get the world to focus on the threat that humanity faces," he said.
The dispute over fishing rights reignited last month when the UK rejected dozens of applications from French boats to fish in UK territorial waters post-Brexit.
Under the trade deal, the EU and UK have agreed they will give licences to boats if they can show they have fished in each others' waters for years.
But there have been disagreements about how much evidence is needed, leading to anger from France when applications were denied by the UK and Jersey.
In May, French boats protested outside Jersey's port and France threatened to cut off the island's electricity supply over what it said were unfair terms.
The view in the UK government is - privately - that this row has rather a lot to do with the fact France is in a tricky election cycle.
They are not entirely surprised that a lot of political hay is being made out of this on the other side of the Channel.
But this is something that has got to be sorted out - and the government is surprised by just how far France has gone in this row, particularly with some of the threats to disrupt cross-Channel trade in the run-up to Christmas.
At that same time, Downing Street does not want to plunge into a huge row about this, it doesn't want to up the ante.
Boris Johnson - who might even see Emmanuel Macron today - is likely to step through this quite carefully because, as he joked yesterday, the UK - with the climate summit in Glasgow coming up - has bigger fish to fry at the moment.
Meanwhile, French President Emmanuel Macron accused the UK of backpedalling on its Brexit commitments over the fishing row and over Northern Ireland.
He told the Financial Times it raised questions about the UK's reliability with the EU and with all of its partners.
"Because when you spend years negotiating a treaty and then a few months later you do the opposite of what was decided on the aspects that suit you the least, it is not a big sign of your credibility," he said.
As well as raising the possibility of retaliation, the UK government has said it could launch "dispute settlement proceedings" with the EU if France went ahead with "unjustified" measures.
