"The sovereign claim to the Malvinas Islands is inalienable," she said in a speech marking the 26th anniversary of Argentina's ill-fated invasion of the islands, located 480 kilometers (300 miles) off shore.
The April 2, 1982 invasion prompted then British prime ministerto deploy naval forces to retake the Falklands, known as the Malvinas in Spanish.
The short, bloody conflict led to Argentina's surrender on June 14, 1982 after the death of 649 Argentines and 255 Britons.
Historians saw the invasion as an attempt by Argentina's ruling military junta, which was then in power, to divert attention away from domestic problems.
In her speech Kirchner called for Argentina to strengthen its representation in international bodies to denounce "this shameful colonial enclave in the 21st century."
And Vice President Julio Cobos said in the southern city ofthat "we must recover this territory that is ours, that belongs to us."
The comments came as Kirchner faces her own woes, battling against farmers who have barricaded roads in a protest against a stiff tax hike on soybean exports.The conflict has created shortages of meat and other staples in and elsewhere,and tested the social fabric, with pro- and anti-government supporters holding dueling rallies.
If it came down to it, do you think Gordon Brown would have the onions to do what Thatcher did the last time?