Speaking at a United Nations Security Council meeting in New York, Ms Fernandez called on Britain to negotiate the archipelago's future.
"We don't take a fanciful approach to the Malvinas," she said, using the Argentine name for the islands.
"We simply want the UN resolution to be enforced."
She was referring to UN Resolution 2065, which urged both parties in 1965 to negotiate.
She said Argentina and Britain should "sit down and discuss" the matter.
Argentina became a non-permanent member of the UN Security Council in January, for a two-year period.
Five of its 15 members (United States, Russia, China, France and Britain) are permanent and have the power of veto.
Argentina has taken over the body's presidency this month, and Ms Fernandez was invited to chair the meeting at the UN headquarters in New York.
She insisted that the islands belong rightfully to Argentina, but called on restraint from both sides.
"This is a litigious and controversial issue. We need to find consensus and safeguard peace."
Britain and Argentina went to war over the islands in 1982.
Margaret Thatcher's government responded to an invasion of the islands on 2 April 1982 by sending a British task force to the South Atlantic.
Some 255 British and 650 Argentine troops died in the conflict, which ended just over two months later, on 14 June, with Argentine surrender.
The islanders voted overwhelmingly on a referendum held in March to remain British.
Argentine President Cristina Fernandez de Kirchner has restated her country's demand for sovereignty of the Falkland Islands.