LONDON — On Thursday, Britain’s prime minister, David Cameron, rebuffed a call by Argentine President Cristina Fernandez de Kirchner to hand over the Falkland Islands, 31 years after the two countries went to war over the South Atlantic archipelago.

‘‘The future of the Falkland Islands should be determined by the Falkland Islanders themselves,’’ Cameron said. ‘‘They’re holding a referendum this year, and I hope the president of Argentina will listen to that referendum and recognize it is for the Falkland Islanders to choose their future, and as long as they choose to stay with the United Kingdom they have my 100 percent backing.’’