Fernandez also criticized member states that don't implement U.N. resolutions, citing unheeded demands for a Palestinian state and Britain's refusal to engage in talks about the disputed Falkland Islands, which Argentina calls the Malvinas.
Argentina holds the rotating Security Council presidency this month and chose as the theme of Tuesday's high-level meeting the relations between the Security Council and regional organizations, which play an increasing role in trying to prevent conflict and restore peace.
It's rare for a head of state to preside over the council, where diplomats usually hold forth. Fernandez arrived 25 minutes late to preside over the meeting, keeping Secretary-General Ban Ki-moon, 14 foreign ministers and dozens of diplomats cooling their heels and chatting.
She said the veto was a safeguard during the Cold War to prevent "nuclear holocaust"—but today the United States and Russia sit at the same table "and we can't deal with the problems in this new world with old instruments and old methods."
Fernandez pointed to two Latin American organizations—the Community of Latin American and Caribbean States and the Union of South American Nations—which take decisions on the basis of unanimity when there is a conflict.
Russia and China have vetoed three Western-backed resolutions to pressure Syrian President Bashar Assad to end the 2 1/2 year conflict that has killed more than 100,000 people, and the United States, Israel's closest ally, has vetoed numerous resolutions over the years on the Palestinian conflict with Israel.
Fernandez strongly supported the Arab League's U.N. observer Ahmed Fathalla who said all 193 U.N. member states must implement U.N. resolutions
This is "the crux of resolving conflicts and central to the effectiveness of the Security Council in settling different matters," she said.
Fernandez cited the Palestinian conflict and the resolution calling for British-Argentine talks on the disputed islands, which Argentina claims Britain has illegally occupied since 1833.
Britain disputes the claim and says Argentina is ignoring the wishes of the island's 3,000 residents who have expressed a desire to remain British, but Argentina maintains that the residents do not have the unilateral right to decide sovereignty over the islands.
Calling for Britain to engage in conversations, Fernandez said "this isn't caprice, it isn't saying we're right. We are just saying that we would like the U.N. resolution to be implemented, that both countries should sit down and discuss a controversial matter."
Britain's U.N. Ambassador Mark Lyall Grant responded in a statement stressing that any discussion must include the Falkland islanders.
"There can be no discussion on the sovereignty of the islands unless and until the islanders so wish," he said, noting that in March the islanders voted overwhelmingly in a referendum to remain part of Britain.
Newly-installed U.S. Ambassador Samantha Power, making her debut at the council, did not comment on the sensitive veto issue. She did say regional organizations are essential to preventing mass atrocities.
She cited the Arab League for sounding the alarm that Moammar Gadhafi's regime "was on the verge of killing thousands of his own people" in Libya, and African Union efforts to help prevent another war between Sudan and South Sudan.
"While U.N. cooperation with regional organizations will remain important, we must also be clear-eyed about its limits," Power said. Although the Arab League "has been at the forefront of pushing for a political transition in Syria, well-known divisions have prevented this council from supporting that effort."
Fernandez and many speakers from Latin America expressed serious concern at reports by NSA leaker Edward Snowden that a U.S. spy program is widely targeting data in emails and telephone calls across Latin America.
Fernandez said she discussed with the secretary-general "the needs to establish regulations of a global nature to ensure and protect sovereignty of states and privacy of citizens in the world."
Brazil's Foreign Minister Antonio Patriota said South American ministers were united in condemning the alleged spying.
Patriota also expressed concern that historically the North Atlantic Treaty Organization, NATO, and its member countries "have considered that the organization does not necessarily require explicit authorization from the Security Council to resort to coercion."