Lord Cameron and Argentinian leader Javier Milei “agree to disagree” over the sovereignty of the Falkland Islands, the Foreign Office has said.
The Foreign Secretary met the Argentine president for talks at the World Economic Forum in Davos.
Mr Milei has suggested a Hong Kong-style agreement which would see the UK hand sovereignty of the islands in the South Atlantic to Buenos Aires.
He said Foreign Secretary and his Argentine counterpart Diana Mondino would “move forward in finding a solution” to the dispute over the islands.
But the Foreign Office made clear the issue of sovereignty was not up for discussion.
A spokesman said it was a “warm and cordial” meeting.
“On the Falkland Islands, the Foreign Secretary and President Milei said they would agree to disagree, and do so politely,” the spokesman said.
“The UK position and ongoing support for the Falkland Islanders’ right to self-determination remains unchanged.”
In a social media post Lord Cameron said the pair discussed “building co-operation on trade and combating global threats” and there was “much that the UK and Argentina can achieve by working together”.
Argentina has long claimed sovereignty over the Falklands and Mr Milei has previously suggested the UK should approach the issue in a similar way to the handover of Hong Kong to China in 1997.
After the meeting with Lord Cameron, Mr Milei was asked by Latin American news website Infobae whether there was scope for a resolution to the Falklands issue based on that model.
“We have not made in-depth progress, but we have made it an item on the agenda for our minister Diana Mondino and minister Cameron to move forward in finding a solution on the topic,” he said, according to a translation.
The Falklands, known as Islas Malvinas in Argentina, were the subject of a bloody conflict in 1982.
The war claimed the lives of 255 British servicemen, three islanders and 649 Argentinian personnel.
UK ministers have repeatedly cited the results of a 2013 referendum which saw close to 100% of voters on the islands, which have a population of about 3,500, opt to remain a British Overseas Territory.
The Falklands are about 8,000 miles from Britain and 300 miles from mainland Argentina.