Argentina's president Cristina Fernandez de Kirchner challenged the British sovereignty of the Falkland Islands on Thursday evening calling it an "affront to the world."
Her demand for negotiation over the islands sovereignty came as the two countries marked 30 years since the end of the Falklands war.
Argentina's president Cristina Fernandez de Kirchner demanded talks over the islands sovereignty
Addressing the UN Committee on Decolonisation in New York on Thursday night, President Kirchner said distance undermined the UK's argument.
"How can it be claimed that, 14,000 kilometres away, that it can be part of the British territory?" she said.
"The UK is benefiting from its privileged position as a permanent member of the security council of the United Nations."
The head of state said the dispute was a challenge to the international community to overcome outdated "prejudice and cliches".
Cameron has said there will be "no negotiation" over the islands
She insisted Argentina just wanted to "talk" about the islands' sovereignty.
"Can someone in the modern world deny that possibility?" she added.
However the Prime Minister told a reception in London that there would be "no negotiation" - and warned that Britain would defend the territory by force again if necessary.
In a speech at the annual Falkland Islands government reception last night, David Cameron said the Falklands was enjoying economic growth and industries such as tourism and fishing were "thriving".
"There is only one shadow on the horizon. And that is the aggression from over the water," Cameron said.
"With Argentina in particular there are so many things we should be working together on - managing fish stocks, increasing trade, environmental issues. This is the kind of co-operation we need - and that's why we want to have a reasonable, sensible relationship with Argentina.
"But let me be equally clear on this - when it comes to the sovereignty of the Falkland Islands, there will be absolutely no negotiation.
"This is not some game of global Monopoly, with nations passing a territory between them. It's about the islanders determining their own future.
"This has been their home for almost 180 years. There are children whose ancestors have lived there for generations. The roots go deep, and they will not be ripped out."
But Kirchner has said the government should feel "shame" for flying the Falklands flag, telling the UN: “When I looked today at 10 Downing Street and saw them and what they were doing with the flag which they call the Falkland Islands flag, I felt shame from afar for them because wars are not to be celebrated nor are they to be commemorated. Do you know why? Because many people lost their lives.”
The comments came after war heroes and those they freed paid a series of moving tributes to the fallen.
Around 400 islanders gathered next to Liberation Memorial in Stanley yesterday to thank those who ended the 74-day occupation of the remote British Overseas Territory.
A thick snow storm began as Falklanders, veterans and VIPs left a service of thanksgiving held at Stanley's Christ Church Cathedral.
Young and old packed into the church with standing room only at the back to take part in the commemoration to those who died in 1982.
The brief but bitter war ended on June 14 1982 as Argentinian commander General Mario Menendez surrendered to the British at Stanley.
The fighting cost the lives of 255 British servicemen, three Falkland Islanders and 655 Argentinian soldiers.
About 30 veterans braved the cold to proudly lead a parade of servicemen from the Royal Navy, the Parachute Regiment, the Royal Air Force and the Falkland Islands Defence Force.
The service was attended by Foreign Office minister Jeremy Browne, who said: "I think it is hard to convey to anybody who isn't here, who is back home in Britain, just how much this means to the Falkland Islanders."
Cameron later highlighted a planned referendum of Islanders on whether they wish to remain linked to the UK. He told the reception: "My message to the government of Argentina is this: the UK has no aggressive intentions towards you. Accusations of militarisation and nuclear threats are hyperbole and propaganda.
"But do not under-estimate our resolve. Threats will not work, attempts to intimidate the islanders will not succeed, because Britain stands ready and willing to stand up for the Falkland Islanders at any time.
"As long as they wish to remain a British territory, that is the way it will stay."