David Cameron has refused to accept a letter from the Argentinian president over the country's claim to the Falkland Islands.
The prime minister spoke to Cristina Fernandez de Kirchner before the first session of the G20 summit on Tuesday, telling her that she should "respect the views" of the islanders who are holding a referendum on control.
Ms de Kirchner attempted to hand Mr Cameron a package marked "UN - Malvinas" but the Prime Minister refused to accept it.
This year marks the 30th anniversary of the Falklands conflict which resulted in a task force being sent to the south Atlantic to successfully reclaim the islands after the Argentinian military junta had invaded the British-held territory.
Britain has rejected calls made by Ms Kirchner to the UN decolonisation committee last week for direct talks to discuss the future of the disputed territory in the south Atlantic.
Downing Street aides said the Prime Minister sought out Ms Kirchner to make Britain's position on the Falklands clear.
Mr Cameron said: "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.
Ms Kirchner was said to have responded with "ramblings" as she tried to hand the PM the envelope stuffed with documents, but Mr Cameron walked away.
In a speech to a business audience in Mexico, he singled Argentina out as an offender over protectionism which he identified as one of the five key threats to global recovery.
Not mentioning Argentina by name, the PM said that there was "one G20 member" which had imposed protectionist measures which threatened to harm the global economy.
There was no doubt that his comments referred to Argentina, which earlier this year sparked fury by nationalising the oil company YPF, largely owned by Spanish firm Repsol.
Mr Cameron said: "In the last eight months investment... has been subject to restrictive measures.
"We have seen the expropriation of a multinational company, requirements that export revenues in oil, gas and mining sectors be exchanged in local financial institutions, new regulations on foreign exchange assets of residents, insurance companies required to repatriate foreign assets and limits imposed on investment in farm land - and that is just from one G20 member."