Hector Timerman brought up the subject of the disputed South Atlantic islands, over which Britain and Argentina fought a war in 1982, during a EU-Latin American summit involving more than 60 countries, they said.
"I can confirm that the prime minister defended the Falklands and their right to self-determination after the Argentine foreign minister raised the issue," a British diplomat told AFP.
He said Timerman made the comments during the plenary session of the summit and that there was no bilateral meeting on the sidelines.
Argentine officials travelling with Timerman confirmed there had been an "incident" during one of the summit's working sessions involving national leaders and ministers, but gave no further details.
Argentine President Cristina Kirchner did not attend the summit.
A report in the Argentine newspaper La Nacion said Timerman had reiterated his government's claim to the islands, which Buenos Aires calls Las Malvinas, to which Cameron replied that his comments were "threatening."
Animosity between Britain and Argentina over the islands has escalated sharply in recent years with the discovery of significant oil deposits offshore.
Argentina claims it inherited the remote, wind-swept islands from Spain when it gained independence.
Britain argues it has historically ruled them and that the islanders should have the right to self-determination.
The 74-day Falklands War claimed the lives of 649 Argentine soldiers, 255 British soldiers and three islanders.