Argentina, which calls the archipelago the Malvinas, claims the British overseas possession as its own, and fought a brief but bloody war for it in 1982.
The islands, she said, "constitute a NATO military nuclear base in the South Atlantic -- this is the truth that they can't continue to hide."
She alleged the archipelago is "among the most militarized areas in the world," saying some 1,500 soldiers and 2,000 civilian military personnel are stationed there amid a population of just 1,000.
Kirchner made the claims during a ceremony honoring the Argentine dead on the 32nd anniversary of the start of the conflict.
Argentine forces invaded the islands on April 2, 1982 but were forced to surrender 74 days later after a British expeditionary force recaptured them.
The fighting that left 649 Argentine soldiers -- many of them conscripts -- dead, along with 255 British personnel and three civilian islanders.