Ceremonies are being held in Israel, Germany, Russia, and other countries to mark International Holocaust Remembrance Day.
At the Vatican, Pope Francis said in a message that people must strive to never let the Holocaust happen again.
The public should "feel the strong desire to work hard so that such horrors, which are a shame for all humanity, might never happen again," he wrote in a letter addressed to Rabbi Abraham Skorka of Buenos Aires, a personal friend of the pontiff.
The message will be read at a violin concert in Rome, where a number of events are being held to observe International Holocaust Day.
Elsewhere, some 60 Israeli lawmakers traveled to Auschwitz-Birkenau, the site of the former Nazi death camp in southern Poland.
They will join hundreds of Israeli and Jewish politicians, as well as Holocaust survivors from around the world, in attending a joint Israeli-Polish ceremony at the site.
Some 20 survivors laid a wreath at the former camp's Death Wall.
Holocaust Remembrance Day on January 27 is also being marked in the German parliament, where President Joachim Gauck is leading the country's lawmakers in a moment of silence to honor the victims of the genocide.
A 95-year-old Holocaust survivor from Russia is set to address the German parliament with a keynote speech.
Russian author Daniil Granin was transported to Auschwitz in 1944 after surviving a Nazi siege of the Russian city of Leningrad, now known as St. Petersburg.
He was among some 7,000 surviving inmates at Auschwitz, which was liberated by Soviet soldiers on January 27, 1945.
WATCH: Moscow's Jewish Museum marks International Holocaust Remembrance Day.
Approximately 6 million Jews were killed in the genocide by Nazi Germany, including more than 1 million people who died in Auschwitz.
In addition to the Jewish victims, International Holocaust Remembrance Day also commemorates other victims of the Third Reich, including the mentally ill, homosexuals, and Roma and Sinti.
European Union foreign-policy chief Catherine Ashton said, "We honor every one of those brutally murdered in the darkest period of European history."
"It is an occasion to remind us all of the need to continue fighting prejudice and racism in our own time," Ashton added in a statement.
In Moscow, diplomats, religious leaders, and public figures will attend a commemoration ceremony at the Jewish Museum and Tolerance Center.
Events were also held in the Russian town of Yantarny, outside Kaliningrad, where Nazi soldiers forced thousands of Jews to march into the ice-covered Baltic Sea in January 1945.
With reporting by dpa, Reuters, AP, and ITAR-TASS