By Shadia Nasralla and Maria Golovnina

LONDON (Reuters) - Prime Minister David Cameron warned Argentina on Tuesday that Britain would always be ready to defend citizens in the remote Falkland Islands after they voted almost unanimously in a referendum to remain British.

Argentina, 300 miles (500 km) to the west of the Falklands, has claimed the South Atlantic archipelago for almost 200 years and in 1982 invaded the islands only to be repelled in a 74-day war with Britain.

British nationals first settled in the Falklands in the 19th century and three decades after the war for ownership of the islands, many still feel strongly about their fate.

"The Falkland Islands may be thousands of miles away but they are British through and through, and that is how they want to stay, and people should know we will always be there to defend them," Cameron said in televised remarks.

"They want to remain British and that view should be respected by everybody, including by Argentina."

In a referendum on Sunday and Monday designed to send a defiant message to Argentina, all but three of those who cast their ballots on the islands voted to remain a British Overseas Territory.

In their ancestral homeland 8,000 miles (12,900 km) away, British television channels ran continuous live coverage from the chilly, windswept and sparsely populated islands over the weekend, and Britons praised the islanders for voting "yes."

"It's a British colony. The settlers out there are all British," Tony Gill, 74, a former military pilot, said in the town of Chelmsford in eastern England.

"They've made the island what it is and now the Argentineans want to take it away from them," added Gill as he headed to a meeting with other veterans, including some of those who fought in the 1982 war.

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Britain pledges to defend distant cousins on Falkland Islands