While Israel's national Holocaust memorial said Abbas' comments may be a step in the right direction, Israeli Prime Minister Benjamin Netanyahu brushed them aside.
He said the Abbas' renewed attempts to reconcile with the Islamic militant movement Hamas raised doubts about the Palestinian leader's intentions. Hamas, a movement sworn to Israel's destruction, has questioned the Holocaust and blocked the subject from being taught in schools in the Gaza Strip.
"President Abbas can't have it both ways. He can't say the Holocaust was terrible, but at the same time embrace those who deny the Holocaust and seek to perpetrate another destruction of the Jewish people," Netanyahu told CNN.
For Abbas, however, conciliatory language marked a breakthrough of sorts.
Denials or attempts to minimize the Holocaust, which saw the systematic killing of 6 million Jews by Nazi Germany in World War II, are widespread in the Arab world.
Many Palestinians fear that if they acknowledge the Holocaust, they will diminish their own claims based on years of suffering, including their uprooting during Israel's 1948 creation and decades under Israeli occupation.
Abbas himself has been accused of minimizing the scope of the Holocaust in a doctoral dissertation in the 1970s, though in recent years he's edged toward acknowledging Jewish suffering.
Abbas' office said he discussed the Holocaust in a meeting with an American rabbi, Marc Schneier, who visited Abbas' headquarters in Ramallah last week.
Abbas told Schneier that "what happened to the Jews in the Holocaust is the most heinous crime to have occurred against humanity in the modern era," according to comments carried by the Palestinian news agency WAFA on Sunday.
The agency quoted Abbas as expressing his "sympathy with the families of the victims and many other innocent people who were killed."
Abbas said the Holocaust was an expression of the idea of ethnic discrimination and racism, and connected it to the Palestinian suffering of today.
"The Palestinian people, who suffer from injustice, oppression and (are) denied freedom and peace, are the first to demand to lift the injustice and racism that befell other peoples subjected to such crimes," he said.
Israel's official Holocaust memorial Yad Vashem said it hoped Abbas' comment may "signal a change" in the Arab world, where "Holocaust denial and revisionism are sadly prevalent." It said it expected Abbas' stance to be "reflected in (Palestinian) websites, curricula and discourse."
Abbas' statement came as the latest U.S. attempt to broker an Israeli-Palestinian peace deal was on the verge of collapse. He urged Israel not to walk away.
"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," Abbas said.
At the start of negotiations in late July, U.S. Secretary of State John Kerry had set an end-of-April target date for a peace deal. He later lowered expectations, calling for the outlines of an agreement and, in a last attempt, for a deal on extending the talks.
However, none of Kerry's objectives appear within reach, and it appears unlikely talks will be salvaged by Tuesday's deadline.
The Palestinian Central Council, a top decision-making body, said in a statement late Sunday that negotiations can only be extended if Israel agrees to a full freeze of settlement construction and commits to the 1967 territorial lines — before Israel's capture of the West Bank, Gaza and east Jerusalem — as a starting point for border talks. Israel has rejected both.
In an apparent hardening of Palestinian positions, the council also said it opposes any land swaps. In previous negotiations, Abbas had accepted the principle of trading some West Bank land for Israeli territory to enable Israel to keep some of the largest Jewish settlements.
The council, which convenes every few years to endorse important decisions, also said it "completely rejects" Israel's demand to be recognized by the Palestinians as a Jewish state. Sunday's statement came at the end of two days of meetings by the council.
Last week, Israel suspended negotiations in response to the Palestinian reconciliation deal. Israel and the West consider Hamas, which has killed hundreds of Israelis in attacks, to be a terrorist group.
"An era has ended and a new era has begun," Cabinet Minister Naftali Bennett, a powerful coalition partner who heads the nationalist Jewish Home party, told foreign journalists Sunday.
"We are not going to reach a peace agreement in the foreseeable future. I think we need to be realistic about what we can achieve."
Instead, Bennett advocating giving the Palestinians "autonomy on steroids" in areas of the West Bank they already control, while annexing the remaining 60 percent of the West Bank that Israel rules.
He said the goal should now to make conditions as livable as possible, by giving Palestinians freedom of movement and supporting their economy, and allowing them to hold elections and run their day-to-day affairs. Full independence, however, would be impossible, he said.
"I know it is not as sexy as the perfect two-state solution but this is realistic," he said.
Abbas said Saturday that any interim unity government with Hamas would be based on his political platform seeking peace with Israel, and not that of Hamas.
Speaking on CBS' "Face the Nation," Tony Blinken, White House deputy national security adviser, appeared to side with Israel's stance that it would not continue peace talks with a Palestinian government backed by Hamas.
"Any Palestinian government has to recognize Israel, it has to renounce violence, it has to accept past agreements," he said.
Associated Press writers Aron Heller in Jerusalem and Karin Laub and Mohammed Daraghmeh in Ramallah contributed to this report.
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