The speech, which Abbas gave at the first meeting of the Palestinian National Council in 22 years on Sunday attributed persecution of Jews to "social behavior" rather than religion.
"It would appear that, once a Holocaust denier, always a Holocaust denier", Netanyahu said on Twitter.
"Apparently the Holocaust denier is still a Holocaust denier", Netanyahu said, calling on the global community to condemn Abbas's "severe anti-Semitism".
However, Abbas has continually called for a two state solution to the Israeli-Palestinian question - essentially supporting Israel's right to exist.
"The speech Palestinian President Mahmoud Abbas delivered on 30 April contained unacceptable remarks concerning the origins of the Holocaust and Israel's legitimacy", a spokesman for the EU's diplomatic service said in a statement.
"This is why attempts to rewrite, downplay or deny it are unsafe", he said.
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Abbas also said that most of Europe's Jews thought their money was more important than their lives because they stayed put.
Abbas backed his story with three points made by Jewish writers and historians, starting with the theory that Ashkenazi Jews are not descendants of the ancient Israelite, and that European Jews therefore had "no historical ties" to the Land of Israel.
Jewish leaders across the political spectrum, both in Israel and overseas, called the history lesson unacceptable. The United States' ambassador to Israel, David Friedman, condemned Abbas' statements, calling them a "new low".
Abbas, 82, has been leader of the Palestinian Authority since November 2004.
After posting a picture from the meeting, Ms Thornberry first said: 'While we of course want to see the resumption of meaningful peace talks, I said President Abbas had been quite right to argue that the Trump administration can not act as a mediator for peace when they themselves are sowing the seeds of discord, and making a negotiated peace ever harder to achieve'.
Abbas was born in 1935 in Safat, a town in the north of what was then British-ruled Palestine. In 1982, Abbas titled his doctoral thesis, "The Other Side: The Secret Relationship Between Nazism and Zionism".