The statement came just days after Israel suspended U.S.-brokered peace talks between the two parties and ahead of the Israel's Holocaust Remembrance Day.
Abbas offered sympathy to the "families of the victims and the innocent people who were killed by the Nazis including the Jews and others."
The Holocaust represents the "concept of ethnic discrimination and racism which the Palestinians strongly reject and act against."
"The Palestinian people are suffering from injustice, oppression and denied freedom and peace, we are the first to demand to lift the injustice and racism that befell on people subjected to such crimes," Abbas added.
Israeli Prime Minister Binyamin Netanyahu responded at a weekly cabinet meeting, saying "rather than releasing declarations aimed at soothing international public opinion, he must choose between Hamas and true peace."
Abbas "made a covenant" with Hamas, which "denies the Holocaust and is attempting to create another Holocaust by destroying the state of Israel," Netanyahu added. "I hope he will escape this covenant and return to the path of real peace."