David Cameron has clashed with Argentina president Cristina Fernandez de Kirchner as the two countries marked 30 years since the end of the Falklands war.
Ms Kirchner used an address to a UN committee to demand talks over the sovereignty of the islands.
But 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.
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 on Thursday 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.
Islanders lined the road next to Stanley Harbour in which HMS Clyde has taken anchor for the commemorations. Union flags were hung alongside the Falkland flag opposite Liberation Monument where an act of remembrance was held. 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.
In a speech at the annual Falkland Islands Government reception, Mr Cameron paid tribute to the bravery of the then prime minister Baroness Thatcher and the armed forces.
"Freedom is only won, and peace is only kept, because there are exceptionally brave people willing to travel to the other side of the world and lay their lives on the line," he said.
"So to everyone who served in the Falklands - those who are here today and those who aren't - I say on behalf of the British people that we are proud of you and we salute you. We will always be in your debt."