The statement comes at a sensitive time for US-led peace efforts, with Israel having suspended faltering talks last week after Abbas reached an agreement with the Islamist Hamas movement to form a unity government.
In a statement in English released just hours before Israel began marking Holocaust remembrance day, the Palestinian leader expressed sympathy with families of the six million Jews who were killed by the Nazi regime.
He also expressed his "sympathy with the families of the victims and many other innocent people who were killed by the Nazis."
The Palestinian leader's remarks, made in a statement following talks with an American rabbi promoting Jewish-Muslim understanding, came as Israel and the Palestinians fought a bitter war of words over the collapse of the peace talks.
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"On the incredibly sad commemoration of Holocaust Day, we call on the Israeli government to seize the current opportunity to conclude a just and comprehensive peace in the region, based on the two states vision, Israel and Palestine living side by side in peace and security," he said.
Abbas has condemned the Holocaust in the past, while some officials from Hamas - which is pledged to Israel's destruction - have either denied or cast doubt on the scope of the genocide.