The 192-nation body declared three years ago that each January 27 will be the International Day in Memory of Holocaust Victims. It was the first time since the end of World War II that the UN recognized the killing of an estimated 6 million Jews and minorities by Nazi Germany.
Germany nominated the day as a national day of commemoration in 1996, while the UN named the date International Holocaust Remembrance Day in November 2005.
On Monday, the assembly will hear addresses by survivors of Nazi death camps, including US Congressman Tom Lantos, and a concert by the Tel Aviv University Symphony conducted by Zubin Mehta. The UN plans also to issue a special stamp to mark the day.
Ban said in a statement in advance of Monday's event that the UN stands in solidarity with Holocaust victims and their families around the world.
"To those who claim that the Holocaust never happened, or has been exaggerated, we respond by reiterating our determination to honor the memory of every innocent man, woman and child murdered at the hands of the Nazis and their accomplices," Ban said.
"We mourn the systematic genocide of one-third of the Jewish people, along with members of minorities, which deprived the world of untold contributions," he said.
He called for a "sense of vigilance" and measures to thwart intolerance from happening again. The UN celebrates this year the 60th anniversary of the Universal Declaration of Human Rights, which Ban said will be an occasion to again remind the world of the Holocaust.
"Let us never take our human rights for granted," he said.
German Chancellor Angela Merkel on Friday said it was a miracle that Jewish life had returned to Germany 63 years after the Holocaust. The chancellor spoke ahead of an international Holocaust remembrance day to be marked Sunday.
Still, during a speech at a conference in Berlin, she voiced concern that "anti-Semitism and anti-foreigner sentiment survive today," and that even educated people were susceptible to crude thoughts and disguised anti-Semitism.
Earlier Friday, in a ceremony commemorating the victims of the Nazi genocide, the President of the German parliament (Bundestag) Norbert Lammert said that it was "shaming" that Jewish institutions still require special police protection.
"We remember an unthinkable crime against humanity and a systematic mass murder," Lammert said.
"After the bitter experiences of the last century, we do not tolerate any kind of extremism, racism and anti-Semitism - nowhere in the world and especially not in Germany," Lammert added.
Excerpts from writings by Czech author Lenka Reinerova were read aloud in the parliamentary session, which was attended by Merkel as well as German President Horst Koehler.
The United Nations established January 27 as an annual Holocaust remembrance day, marking the anniversary of the liberation of the Auschwitz death camp in Poland.
The day, which falls on a Sunday this year, was marked across Germany on Friday.
Former Israeli ambassador to Germany Avi Primor praised the way the country has confronted its Nazi past, saying at the state parliament of Thuringia "where have you ever in the world seen a nation that puts up memorials to commemorate its own shame?"
"Only the Germans have had the courage and the humility," he added.
Writing in the national daily Sueddeutsche Zeitung Friday, the president of the World Jewish Congress, Ronald Lauder, said the Holocaust had led directly to the founding of the state of Israel.
"The existence of Israel as a Jewish state continued to be questioned in Europe, even though Israel was the only country in the region that had maintained a stable democracy for 60 years," Lauder said.
Lauder warned against ignoring the dangers from Iran and its nuclear program.