David Cameron has refused to accept a letter about the Falkland Islands from Argentina's President Cristina Fernandez de Kirchner at the G20 summit in Mexico.
The pair came face to face during the first working session involving leaders of the 20 countries.
The Argentine lobby briefed reporters that Mr Cameron declined to talk to Ms Fernandez about the sovereignty of the islands .
He told her she should "respect the views" of islanders, who are due to hold a referendum on the archipelago's political status.
Ms Kirchner's envelope is said to have contained around 40 or so United Nations resolutions on the Falklands.
Downing Street aides said the Prime Minister sought out the Argentine President to make Britain's position on the Falklands clear.
Mr Cameron told her: "I am not proposing a full discussion now on the Falklands but I hope you have noted that they are holding a referendum and you should respect their views.
"We should believe in self-determination and act as democrats here in the G20."
Aides said Mr Cameron gave a "clear and calm message" which he repeated three times as his words were interpreted into Spanish.
Later, at a news conference, Mr Cameron said it was important to stand up for the Falkland Islanders and put the issue beyond doubt.
"I think this referendum is a very important moment and I wanted to raise it specifically with the Argentine president and say it's important that everyone pays attention to this referendum. So I think it was the right thing to do."
Argentine foreign minister Hector Timmerman confirmed it was Mr Cameron who approached the Argentine president.
"The one that came forward trying to talk about an issue that wasn't on the agenda was Prime Minister David Cameron," he said.
"The right time to talk about this issue was last week when the UN summoned the UK and Argentina to talk at the decolonisation committee, and once again Great Britain declined the offer to be there."
Britain has repeatedly rejected calls for talks on the sovereignty of the Falklands, which Argentina calls Las Malvinas, pointing out that the islands are self-governing.
The islands' 3,000 inhabitants are planning a referendum on whether they want to stay part of Britain's self-governing overseas territories, a step designed to outflank Argentina's sovereignty claims.
The confrontation came after Mr Cameron criticised Argentina for undermining attempts to restore global growth through protectionist measures on trade.
Speaking to a business audience ahead of the official opening of the Los Cabos summit, Mr Cameron did not mention Argentina by name, but said that there was "one G20 member" which had imposed protectionist measures which threatened to harm the global economy.
There was no doubt his comments referred to Argentina, which earlier this year sparked fury by nationalising the oil company YPF, largely owned by Spanish firm Repsol.
Buenos Aires has also imposed new requirements on the movement of financial assets designed to shore up its own economy.