Cristina Kirchner described the prime minister as "arrogant" and said his comments were an "expression of mediocrity and almost of stupidity".
Cameron had been prompted by Conservative MP Andrew Rosindell during prime minister's questions to remind Barack Obama that the British government would not accept any kind of negotiations over the south Atlantic islands, which Argentina and Britain fought a 10-week war over in 1982.
Cameron told the Commons: "I would say this: as long as the Falkland Islands want to be sovereign British territory, they should remain sovereign British territory – full stop, end of story."
In her criticism of his comments, Kirchner said that Britain "continues to be a crude colonial power in decline".
She has insisted that the two countries should negotiate over the islands, which have been a British territory since 1833. The 1982 conflict cost the lives of 649 Argentinian and 255 British troops. It ended when the invading Argentinian forces surrendered on 14 June, now celebrated by the islanders as liberation day.
