"There is no German identity without Auschwitz," Gauck said before the packed chamber, where survivors of the death camp in Nazi-occupied Poland sat watching MPs, government ministers and Chancellor Angela Merkel.
"The memory of the Holocaust remains a matter for every citizen who lives in Germany. It belongs to the history of this country."
He said the "moral duty" for Germany was not only to remember the past but also what he termed the "mission" to protect and preserve humanity and every individual's rights.
"We say that precisely in times when, we in Germany, again have to agree on cooperation between different cultures and religions.
"The community in which we all want to live will only thrive where the dignity of the individual is respected and where solidarity is alive," Gauck added.
President (Speaker) of the Bundestag Norbert Lammert said that Auschwitz had become a synonym for humankind's potential for cruelty.
Remembering the Holocaust also meant that similar crimes could never be permitted anywhere in the world, he said.
"Later generations aren't responsible for the horrific past of our country," Lammert concluded.
"But they do answer for how we deal with it."
Gauck was due to join other world leaders and 300 survivors for a commemorative ceremony at the site of the Auschwitz death camp later on Tuesday.
SEE ALSO: Germany remembers horror of Auschwitz
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