Britain and Argentina fought a 10-week war in 1982 over the remote South Atlantic islands, which are part of Britain's self-governing overseas territories and are known in Argentina as Las Malvinas.
Fernandez has marked the 30th anniversary of the conflict with a sustained diplomatic campaign to assert Argentina's sovereignty claim, whose significance has been raised by oil exploration in the waters around the islands.
In her letter, published in British newspapers, Fernandez accused Britain of breaching United Nations resolutions urging the two countries to negotiate a solution to the dispute.
"The question of the Malvinas Islands is also a cause embraced by Latin America and by a vast majority of peoples and governments around the world that reject colonialism," Fernandez wrote.
Cameron rejected her call for negotiations, sticking to London's stance that the approximately 3,000 people of the Falkland Islands had chosen to be British.
"The future of the Falkland Islands should be determined by the Falkland Islanders themselves," he said. "Whenever they have been asked their opinion they have said they want to maintain their current status with the United Kingdom."
The islanders are expected to vote overwhelmingly in favour of the existing arrangement in a referendum this year.
"I hope the president of Argentina will listen to that referendum and recognise it is for the Falkland Islanders to choose their future," Cameron said.
"As long as they choose to stay with the United Kingdom, they have my 100 percent backing," he added.
Fernandez said her open letter was timed to coincide with the 180th anniversary of the day when Argentina was "forcibly stripped" of the islands in what she called a "blatant exercise of 19th century colonialism".
Noting that the islands are 14,000km from London, Fernandez accused Britain of expelling Argentines from the territory and carrying out a "population implantation process".
Britain disputes this, saying no civilian population was expelled from the Falklands on or after January 3, 1833.