David Cameron today pledged Britain would never surrender sovereignty of the Falklands against the wishes of the islanders.
In his Christmas message to the islands, the Prime Minister said he could not accept challenges by Argentina to their right to self-determination.
He condemned what he described as "unjustified and counterproductive" efforts by the government in Buenos Aires to disrupt shipping links to the islands.
His intervention comes after Argentina led a group of South American nations in banning ships flying the Falklands flag from docking at their ports.
In his message, Mr Cameron declared: "Whatever challenges we face in the UK, the British Government's commitment to the security and prosperity of the overseas territories, including the Falklands, remains undiminished.
"So let me be absolutely clear. We will always maintain our commitment to you on any question of sovereignty. Your right to self-determination is the cornerstone of our policy.
"We will never negotiate on the sovereignty of the Falkland Islands unless you, the Falkland Islanders, so wish. No democracy could ever do otherwise."
The ban on Falklands-flagged ships by the Mercosur bloc - which also includes Brazil, Paraguay and Uruguay - is the latest flare-up between Britain and Argentina over the islands.
Buenos Aires - which has long claimed sovereignty over the territory it calls the Malvinas - reacted angrily last year when Britain allowed offshore drilling for oil in the islands' waters.
The Argentinians were also irritated by the recent announcement of Prince William's forthcoming RAF posting to the islands.
Mr Cameron insisted he wanted a "constructive relationship" with Argentina, but said that its attitude to the Falklands was unacceptable.
"Argentina continues its unjustified and counterproductive efforts to disrupt shipping around the islands and to deter business from engaging in legitimate commerce," he said.
"Threats to cut communication links between the islands and your neighbours in South America only reflect badly on those who make them.
"I firmly believe that it is in our interests that we have a constructive relationship with Argentina. There is common ground to be found on issues like the global economy and climate change.
"We want to work with Argentina on those issues. But the Argentine government has continued to make statements which challenge your right to self-determination, and we can never accept that."