"I made this poster because anti-Semitism is a big problem in Europe," said Neumann, who was an 8-year-old boy when he was freed from the camp. Originally from Slovakia, he lost a grandmother at Auschwitz.

"But she has no grave," he said. "I am happy there is snow here because it keeps me from standing on her ashes."

Putin compared the Nazis with modern terrorists.

"Today we shall not only remember the past but also be aware of all the threats of the modern world," he said. "Terrorism is among them, and it is no less dangerous and cunning than fascism."

Earlier in Krakow, Cheney noted that the Holocaust did not happen in some far-off place but "in the heart of the civilized world."

"The story of the camps shows that evil is real and must be called by its name and must be confronted," he said.

People at the ceremony expressed concern over recent incidents such as a walkout from an Auschwitz commemoration by far-right local legislators in Germany, and a statement from far-right National Front leader Jean-Marie Le Pen in France, who minimized the brutality of Nazi rule during the occupation by German troops. He said it "was not particularly inhuman, even if there were a few blunders."

Camp survivor Franczisek Jozefiak, 80, said the world still needed reminding.

"Today I'm remembering my father, gassed here. I'm remembering the atrocious things they did to us here," said Jozefiak, who is from Krakow.

The Nazi guards lined them up and told some to go right, others left, he said. Jozefiak went left and his father went right and was taken to the gas chamber.

"The message today is: No more Auschwitz," he said. "But the world has learned nothing so far — you see they are fighting and killing each other everywhere in the world.

"Today they are saying a lot because of the anniversary, but tomorrow they will forget," he said.