Argentina's President Cristina Fernandez de Kirchner has demanded that Britain enter negotiations over the sovereignty of the Falkland Islands.
President Fernandez was addressing the UN Committee on Decolonisation on the 30th anniversary of the UK territory's liberation from Argentine occupation.
She said history and geography backed Argentina's claim. But an islander told the committee Argentina was "bullying".
UK Prime Minister David Cameron has said there would be "no negotiation".
Earlier on Thursday, the Falklands marked the end Argentina's 74-day 1982 occupation with a service at Port Stanley's Christ Church cathedral.
Veterans of the war then led a military parade to the Liberation Monument for an act of remembrance, paying tribute to the 255 UK servicemen and three Falklands civilians who died in the war.
An estimated 650 Argentines were also killed during the conflict.
The BBC's Barbara Plett said President Fernandez made as much as she could of her platform at the United Nations, where a majority backs Argentina's demand that the Falklands' status be negotiated.
The president was accompanied by more than 90 delegates and raised the diplomatic stakes by travelling to New York personally on the sensitive anniversary of the islands' liberation, our correspondent said.
President Fernandez said that the Malvinas - as Argentina refers to the islands - formed part of the South American continental plate.
"How can it be claimed that, 14,000 kilometres away [8,700 miles], that it can be part of the British territory?" she asked.
"The UK is benefiting from its privileged position as a permanent member of the security council of the United Nations," she said.
"The issue of the Malvinas is a challenge to see whether or not we are capable of overcoming prejudice and cliches that are outdated, because the world has changed and there are new players."
President Fernandez said Argentina was "just asking to talk" about the islands' sovereignty and the fact they were still under British rule was "an affront to the world which we all dream of".
'Lust for lands'
Two Falkland Islands legislators also spoke at the same session, where they insisted on their right to self-determination.
Legislator Mike Summers said Falkland Islanders had a "distinct and clear identity" and considered the islands to be their country and home.
"As much as Argentina might like to airbrush us out of existence to satisfy its unjustified lust for our lands, such behaviour belongs to another era and should not be tolerated in the modern world," he said.
Mr Summers tried to pass a letter offering talks with the Falklands government to President Fernandez but could not get close enough.
Argentina's foreign minister refused to take the document telling the legislator to "send it to my embassy".
In a speech at the Falkland Islands Government reception on Thursday evening, David Cameron spoke of "aggression from over the water".
"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," he added.
"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."
Mr Cameron paid tribute to the bravery of those who served in the Falklands and said Britain would always be in their debt.
Foreign Office minister Jeremy Browne attended the service in Port Stanley. He said it was "hard to convey" to the wider world "just how much this means to the Falkland Islanders".
"There are hundreds of people gathered here in what is frankly really freezing cold, inhospitable weather, and they are doing that because they are so grateful for what we achieved on their behalf 30 years ago," he said.
In London the Falklands' flag flew over government buildings.