The talks between Mr Brown and Ms Fernandez were 'constructive'
Gordon Brown has rejected calls from Argentina for talks over the future sovereignty of the Falkland Islands.
The prime minister turned down a request for discussions on the islands' status at a meeting with Argentine president Christina Fernandez.
The two met for talks in Chile, where Mr Brown is meeting leaders ahead of next week's London G20 summit.
Argentina has maintained claims to the islands, over which both countries went to war in 1982.
Speaking after the meeting, Argentine Foreign Minister Jorge Taiana said Ms Fernandez had pressed the issue of the Falkland Islands, which are referred to in Spanish as the Malvinas.
'Differences of opinion
"The president stated with great clarity and firmness the need for the United Kingdom to do what the United Nations has asked and to hold talks to find a solution to a sovereignty conflict between the United Kingdom and Argentina over the Malvinas," Mr Taiana said.
A British official said Mr Brown had "set out the British government's long-standing position on sovereignty in very clear terms".
"He emphasised the importance of self-determination. Both sides agreed that they have differences of opinion," the official said.
Mr Brown and Ms Fernandez touched on the issue of the Falkland Islands for 15 minutes during their meeting, which lasted for almost 40 minutes.
The two leaders also discussed flights between Argentina and the Falkland Islands, during negotiations which were described by Britain as "constructive".
G20 LONDON SUMMIT
World leaders will meet next week in London to discuss measures to tackle the downturn. See
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to the G20 summit.
The G20 countries are Argentina, Australia, Brazil, Canada, China, France, Germany, India, Indonesia, Italy, Japan, Mexico, Russia, Saudi Arabia, South Africa, South Korea, Turkey, the United Kingdom, the US and the EU.
The Argentine talks came after the prime minister visited Strasbourg, New York, Brazil and Chile in an attempt to drum up support before the G20 meeting.
On Friday, Chile's president Michelle Bachelet told Mr Brown her country had "saved in the good times" in order to spend in the bad.
BBC political editor Nick Robinson said Ms Bachelet's comments echoed Tory criticisms and she appeared to be unaware of how unwelcome they would be.
Ms Bachelet warmly endorsed Mr Brown's leadership of the G20 and his efforts to seek a global solution to global economic problems, our correspondent said.
She also called for those countries involved to agree to a co-ordinated fiscal stimulus at their conference in London next week.
But she went on to say that because of decisions made in the good times, Chile had prepared for the bad.
Mr Brown responded by insisting that the International Monetary Fund believed the UK was better prepared than most countries for the economic crisis.
During Mr Brown's visit to Brazil, the Brazilian president Luiz Inacio Lula da Silva raised eyebrows when he claimed the financial crisis was caused by "white, blue-eyed people".