UN Secretary-General Kofi Annan noted the mass abuses of human rights in Sudan's Darfur region, where tens of thousands of civilians have died.
He said an upcoming report from a commission he formed to investigate genocide would pose an immediate challenge to the UN Security Council to act.
"We rightly say, 'never again,' but action is much harder," Annan said. "Since the Holocaust the world has, to its shame, failed more than once to prevent or halt genocide -- for instance in Cambodia, in Rwanda, and the former Yugoslavia."
Dozens of top government officials addressed the session but the General Assembly hall, usually crowded during special sessions, was less than half full. Aside from Israel, just one other Middle East country -- Jordan -- was due to speak.
Holocaust survivor Elie Wiesel told the session the evils of Auschwitz, the largest Nazi death camp, continue to defy "language and understanding." Wiesel said it was incomprehensible that a modern nation such as Germany could be capable of setting up camps where 6 million Jews died.
"The question remains open: In those dark years, what motivated so many brilliant and committed public servants to invent such horrors?" Wiesel said.
Israeli Foreign Minister Silvan Shalom said there was a revival of anti-Semitic attacks against Jews and Israel. In some ways, he said, the new attacks paralleled the hate propaganda of 1930s Germany.
"The brutal extermination of a people began, not with guns or tanks, but with words, systematically portraying the Jews -- the others -- as less than legitimate, less than human," Shalom said.
The United States was represented by Paul Wolfowitz, the deputy defense secretary, who cited the necessity of war to end the horrors perpetrated by Germany.
Wolfowitz, an architect of the war to oust Iraqi leader Saddam Hussein, said through history Americans had waged war only "as a duty when it was necessary." He said the world must continue to act when confronted with barbarities like the Nazi death camps.
"Never again and never forget," Wolfowitz said. "We must keep remembering, we must continue to speak about unspeakable things, so we commend the UN for this remembrance of the Holocaust befitting its significance in human history. In doing so, can perhaps can avoid such inhumanity and the warfare that marches along with it."
Yesterday's session at the UN was part of a series of events leading up to the 27 January commemoration of the actual anniversary of the liberation of Auschwitz in southern Poland.