David Cameron has called on Argentina to respect the wishes of the people of the Falkland Islands after they voted overwhelmingly for the territory to stay British in an unsurprising but still historical referendum that aims to send a defiant message to Argentina and the outside world.

The prime minister said Argentina should take "careful note" of the referendum result and that Britain would always be there to defend the Falkland Islanders.

Despite near zero temperatures and flurries of snow and rain, the turnout was 92% from an electorate of 1,650. All but three people voted yes to the question posed on the ballots: "Do you wish the Falkland Islands to retain their current political status as an overseas territory of the United Kingdom?"

Nobody expected anything but a landslide in a vote that the Argentinian government had dismissed as illegal. Regardless, the islanders said they were delighted at the strong show of unity at a time when the Falklands are coming under increasing pressure from Buenos Aires and its allies in South America.

"I'm very happy. Everyone has come together to express ourselves," said Kyle Biggs, who guides tourists to see penguins and battlefield sites from the 1982 war between Britain and Argentina. "I think this is massively significant. It's important to show how much we want to stay British."

After the results were announced, Biggs said, islanders celebrated late into the night (video) despite temperatures of 3C.

In Argentina the result was dismissed with angry words by the government of President Cristina Fernández de Kirchner. "We must denounce this trickery that pretends to represent the popular participation of an implanted population," said Senator Daniel Filmus, a close collaborator of the president. "This publicity stunt has no validity for international law."

Argentina's Senate is preparing to vote this week on a motion to reject the Falklands referendum and reaffirm Argentina's longstanding claim to the islands it calls Las Malvinas. "The United Kingdom lacks any right at all to pretend to alter the juridical status of these territories even with the disguise of a hypothetical referendum," said Argentina's foreign minister, Hector Timerman.

Another close Kirchner collaborator, Senator Anibal Fernandez, restated the government's view of the Falklanders as a foreign population living illegally in Argentina. "There will never be self-determination for an implanted population and there is no legal framework for this, the Malvinas are Argentine sovereign soil," said Fernandez.

Speaking to an Argentinian radio station, the country's ambassador to London, Alicia Castro, suggested the islands need Argentina to guarantee their survival. "How long can the islanders live isolated from the continent? They are 8,000 miles from London and 500 kilometres from continental Argentina," Castro told the Buenos Aires radio station La Red.

Cameron insisted that the islanders were entitled to the right to self-determination. "It is the clearest possible result there could be," he said.

"The Falkland Islands may be thousands of miles away but they are British through and through and that is how they want to stay. People should know we will always be there to defend them.

"We believe in self-determination. The Falkland Islanders have spoken so clearly about their future and now other countries right across the world, I hope, will respect and revere this very, very clear result."

The Falklands have moved back into the international spotlight due to the 30th anniversary of the war and a push by President Kirchner to reassert her country's longstanding sovereignty claims.

Argentina has raised the issue at the UN and regional bodies, placed full-page advertisements in British newspapers and – most controversially – restricted access to the islands. It has persuaded South American neighbours to turn away Falklands-flagged ships, curtailed overflights and imposed sanctions on companies that exploit the resources of the islands.

The islanders have a high degree of legislative autonomy, although they are still under a governor sent by London. They organised their first ever referendum to show their determination to resist what some of them say is a blockade.

Mike Summers, a member of the Falklands' Legislative Assembly, told the Guardian before the election that Argentina had become "aggressive and difficult".

"Our relationship with the UK is strong and mutually productive, and we would like to be left in peace to continue to develop that relationship for the benefit of future generations," he said.

The British foreign secretary, William Hague, said the referendum result demonstrated more clearly than ever the Falkland Islanders' wish to remain an overseas territory of Britain. "All countries should accept the results of this referendum and support the Falkland Islanders as they continue to develop their home and their economy. I wish them every success in doing so," he said.

The vote is unlikely to shift opinion in Argentina. In 2012 a poll to mark the 30th anniversary of the war indicated that 89% of Argentinians support the sovereignty claims of Buenos Aires. Many believe the timing of the referendum is linked to the discovery of extensive oil and gas deposits, as well as growing interest in the Antarctic, which is likely to become an important source of fresh water and other resources. Veterans say it is absurd that the small community of islands should decide the fate of an strategically important area of land and sea that is bigger than Argentina itself.