Abbas also reiterated his support for Egypt's efforts to mediate a truce between Israel and Hamas militants in the Gaza Strip.
"Despite all the circumstances we're living through and all the attacks we're experiencing, we insist on peace. There is no other path," Abbas said in a speech marking International Women's Day.
Israel has sent mixed signals since Thursday night's shooting, in which a Palestinian gunman burst into a prestigious Jerusalem seminary and killed eight students, many of whom were studying religious holy texts in the building's library.
Officials have indicated a willingness to move ahead with peace talks with Abbas, launched last November at a U.S.-hosted summit in Annapolis, Md. The sides hope to reach a final agreement by the end of the year. The Egyptian-backed truce efforts remain more cloudy, especially if it turns out that Hamas was behind the seminary shooting.
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Israeli government spokesman Mark Regev said Israel "remains committed to the Annapolis framework." But he said there were no decisions on when talks would resume.
"We believe in historic reconciliation with the Palestinians. One of the foundations of Annapolis was no tolerance of terrorism. The best way to move forward is for the Palestinian side to be a real partner, not only in talks, but in helping to fight this sort of hateful extremism we saw this week," he said.
The U.S. has said extremist violence should not be allowed to derail peace talks.
Earlier this week, Abbas suspended the talks to protest an Israeli offensive in the Gaza Strip that killed more than 120 Palestinians, including dozens of civilians. Israel launched the offensive to halt intensifying rocket fire from Gaza, which is controlled by the Hamas militant group. Abbas later backed down under heavy U.S. pressure.
Palestinian negotiator Saeb Erekat said peace talks are expected to resume on Thursday with the arrival of U.S. Lt. Gen. William Fraser III for a joint meeting with Israelis and Palestinians. Fraser is supposed to monitor the sides' compliance with the "road map," a U.S.-backed peace plan.
Regev said the Fraser meeting still was not definite.
Separately, Egypt, backed by the U.S., is exploring a truce deal between Israel and Hamas that would stop rocket fire on Israel in exchange for an end to Israeli attacks on militants and the resumption of trade and travel from Gaza, where border crossings have been closed since Hamas violently seized control of the coastal strip in June.