Argentinian protesters have burned The Sun and Union Jack in Buenos Aires as Falkland Islanders wrote an open letter to the country's president.
Copies of the newspaper advert and the flag were torched at a cruise terminal in the capital after British Prime Minister David Cameron rejected calls for talks on the disputed territory.
A group of the islanders, called Falklands United, responded on Friday to a letter by Cristina Fernandez de Kirchner published in The Guardian and Independent in which she called for the UK to give up the Falklands.
They wrote: "Our home is a British Overseas Territory, not a colony as you seemingly wish to convince people.
"We have never been prouder of our association with the United Kingdom and our unique relationship.
"Any decision to change that would be OUR and not YOUR choice.
"In 1982 we didn't have a voice. In 2013 we do. We are OUR own people and we have a right to OUR own democracy and to where OUR sovereignty lies."
It comes after a British tabloid published a full page newspaper advert in Argentina, warning Ms Kirchner to keep her "hands off" the Falklands.
The Sun was responding to Ms Kirchner's open letter, in which she called for the islands to come under Argentine sovereignty.
A referendum on the islands' status is to take place in March.
Mr Cameron has insisted that residents of the Falkland Islands must decide their own future.
The Sun's message to Ms Kirchner - printed in English language paper The Buenos Aires Herald - raises the issue of Argentina's 1982 invasion of the islands.
It mentions the 649 Argentine and 255 British servicemen who lost their lives and says the invasion was in "direct conflict" with the UN principle of self-determination.
The ad in the paper - read by some 50,000 people - disputes Argentina's claim to the islands and points out that British sovereignty dates back to 1765.
It concludes: "Until the people of the Falkland Islands choose to become Argentinian, they remain resolutely British.
"In the name of our millions of readers and to put it another way: 'HANDS OFF!'"
Ms Kirchner's open letter was published in The Guardian and Independent and called for the UK to give up the Falklands - known as Las Malvinas in Argentina.
She urged Mr Cameron to abide by a 1965 UN resolution to "negotiate a solution" to the dispute.
But the PM told the leader that she should "listen" to the result of the March referendum.
He said: "The future of the Falkland Islands should be determined by the Falkland Islanders themselves, the people who live there.
"Whenever they have been asked their opinion, they say they want to maintain their current status with the United Kingdom.
"They're holding a referendum this year and I hope the president of Argentina will listen to that referendum and recognise it is for the Falkland Islanders to choose their future."