The United Nations General Assembly last November declared that January 27 would be its official memorial day for the Holocaust -- the systematic slaughter of an estimated six million Jews, as well as other groups, during World War II.
On a clear, cold day on Friday at Auschwitz Polish Prime Minister
Kazimierz Marcinkiewicz placed a wreath and bowed his head at the foot of the main memorial in honour of the 1.5 million people who died at the Nazi-run camp.
Mr Marcinkiewicz was joined by the Israeli ambassador to Poland, camp survivors and representatives of the Jewish community.
Soviet troops liberated Auschwitz and the neighbouring Birkenau camp on January 27, 1945, as World War II neared its end.
Some 1.5 million people, most of them Jews, died there from gassing, starvation, exhaustion, beatings and disease between 1940 and 1945.
Other victims included Soviet prisoners of war, Poles, Gypsies, homosexuals and political opponents of the Nazis.
In Warsaw an empty tramcar bearing the Star of David in place of a number rolled silently through the streets, identical to one that in the 1940s travelled through the Warsaw ghetto, which was annihilated by the country's Nazi occupiers during the war.
In Prague, Auschwitz survivor Felix Kolmer urged people to look ahead as well as back.
"Let's not forget that memories of our suffering have to also be a point of departure for creating a better future," said Mr Kolmer, 83.
Several leaders used the occasion to reject Iranian President Mahmou Ahmadinejad's recent statement that Israel should be wiped off the map and his description of the Holocaust - the murder of six million Jews by the forces of German dictator Adolf Hitler - as a "myth".
Germany's parliamentary president Norbert Lammert said the lessons of the Holocaust should continue to influence national policy, referring to Mr Ahmadinejad’s remarks.
Mr Lammert stressed that the need to commemorate the millions of Jews and other victims murdered by the Nazis would not diminish with time.
"We want to - and we must - continue to be prepared to learn from our history," he said at a special session of parliament.
"With dismay we have had to note that today, even presidents insist on describing the Holocaust as a fairy tale and go so far as to make anti-Semitic remarks,” he said.
Germany has joined other nations in expressing concern about President Ahmadinejad's comments.
In a statement released at the United Nations European headquarters in Geneva, UN Secretary-General Kofi Annan said it was imperative the world remember the unique tragedy of the Holocaust and reject all attempts by "bigots" to deny the extermination of the Jews during World War II.
"It must be remembered, with shame and horror, for as long as human memory continues," Mr Annan said in the statement, released to mark the first international day commemorating the victims of the Holocaust.
Meanwhile, Poland's powerful Roman Catholic Church called on believers to light candles in their windows in memory of those who perished in the Holocaust.
Other memorials
In Estonia, invaded by German troops in 1941, the government issued a statement on the eve of Holocaust memorial day saying it was "regrettable" that some Estonians collaborated with the Nazi occupiers in perpetrating crimes against humanity.
The Nazis sent up to 10,000 Jews from other countries to camps set up in Estonia, most of whom died in the Baltic state.
In Lithuania, the ambassadors of Britain, Germany, Poland, Russia, the United States and other officials gathered at a memorial at Paneriai, close to the capital Vilnius, on Friday morning to listen to prayers.
Paneriai was the site of a Nazi death camp 1941-1943 where some 100,000 people, mainly Jews, were killed.
In Belgrade, where 5,000 Jews and Roma died in a concentration camp, Serbian Prime Minister Vojislav Kostunica officially opened a monument to the memory of victims.
In Italy, a ceremony presided by Foreign Minister Gianfranco Fini marked the publication of a book about some 400 Italians who saved Jews from 1943 to 1945 during Nazi occupation.
Council of Europe chief Terry Davis warned that "61 years after the liberation of Auschwitz, Europe is not yet free of racism, anti-Semitism, prejudice against Roma or homophobia.
"We need deeds, not words" to fight discrimination, he said.
Ceremonies also took place in the Czech Republic, Finland, Spain and Sweden, while in Norway the education minister was to award an annual prize to the school that has been most active in fighting racism and anti-Semitism.