Events have taken place at Auschwitz to commemorate the 65th anniversary of the liberation of the Nazi death camp, as the world marks Holocaust Memorial Day.
Elderly survivors gathered in freezing weather in Poland, where the camp was built under German occupation.
Israel's prime minister and president urged that the Holocaust should never be forgotten, mourned its dead, and warned of a new danger posed by Iran.
More than a million people were murdered by the Nazis at Auschwitz.
The great majority were Jews but they also included non-Jewish Poles, Roma Gypsies and Soviet prisoners of war.
The camp was liberated by the Soviet Red Army on 27 January 1945.
At least six million Jews were killed by the Nazis during World War II.
Speaking in a tent pitched amid snowy conditions at Birkenau death camp, next door to Auschwitz, Israeli Prime Minister Benjamin Netanyahu said: "We sit in a warm tent, we remember those who shivered to death, and if they didn't freeze to death they were gassed and burned in a horrible conflagration.
"And we remember too that one third of the righteous of the nations - those who risked their lives and more so risked the lives of their children and their families to save others - were Polish people. We remember that."
Earlier, speaking to reporters, Mr Netanyahu said the Jewish people - unlike 65 years ago - were now prepared for any new threat to destroy them, and that Israel was "a country that is able to alert the nations of the world to the danger".
His comments were widely perceived as referring to Iran, though he did not mention it by name.
In Berlin, addressing Germany's parliament, Israel's President Shimon Peres was more explicit, drawing parallels between Nazi Germany and present-day Iran, which he called a "fanatical regime" and "a danger to the entire world".
Reflecting on the Holocaust, he said some of those who carried it out "still live on German and European soil, and in other parts of the world".
"My request of you is: Please do everything to bring them to justice," he told German MPs.
Mr Peres also recalled leaving his grandfather behind in Poland, when his family moved to Palestine in 1934. His grandfather was later killed by the Nazis - herded into a synagogue with the other Jews of his village, and burned to death.
"I remember his poignant embrace. I remember the last words and the order I heard from his mouth: 'My boy, always remain a Jew'," he said.
Some of those who survived the Holocaust gathered at Auschwitz on Wednesday, many with their relatives.
They passed beneath the notorious sign above the entrance, reading "Arbeit Macht Frei", or "Work Makes You Free".
The sign is a replica. The original was stolen last month. It has been recovered, in three pieces, but not yet repaired and repositioned.
August Kowalczyk spent two years at Auschwitz and survived.
"This place determined who I am today, aged nearly 90," he said.
"I still have one mission - to pass on to the next generation knowledge of what happened here."