Palestinian Authority President Mahmoud Abbas has agreed to resume peace talks with Israel without prior conditions, a senior PA official said Tuesday, even as a rocket attack on Ashkelon revived concern of renewed violence in the South. The attack struck hours after Prime Minister Ehud Olmert left the city. No damage was caused by the projectile, which hit during a period of relative calm in the South. The recent firing of Grad missiles at Ashkelon should not be considered a one-time event, Olmert told city council members during a visit that also took him to an elementary school, Barzilai Hospital and the home of the Givati Brigade's Sgt. Liran Banai, 20, who was fatally wounded by a roadside bomb outside the central Gaza Strip on Thursday. "This is the reality of the past 60 years and we must show restraint and strength," Olmert told the Ashkelon city council members. Ashkelon should not be compared to Sderot, which had been under continual rocket attack for years, the prime minister said. "True, the Grad is heavier than the Kassam, but we have no way to prevent these things from happening again. We have to deal with them," he said. Responding to reports that Hamas had ceased firing rockets on Israel because of an agreement brokered by the Egyptians, Olmert said, "Maybe the reason they are not shooting is not out of a love of Israel, but because they have control over the rocket launchers. They are also hurting from when we hit them hard and are rethinking, but that doesn't mean they will not start again." "We have no desire to strike at Gaza's residents," Olmert said. "We are doing this because of a reality that leaves us no other choice, so that their pain will be such that it makes them stop." He said Israel was systematically fighting terrorism. "There is no place in the country that is not important and that we won't defend," Olmert said. "Israel faces a difficult reality that we deal with while gritting our teeth." Despite Tuesday's attack on Ashkelon, defense officials said it appeared Hamas would continue to enforce a cease-fire policy. The officials said the IDF would be allowed to strike at targets in Gaza if terrorists were spotted planning or perpetrating an attack. The officials said there was concern Hamas would use the period of quiet to rebuild its military wing, which suffered severe losses during fighting with the IDF last week. Close to 100 Hamas gunmen were killed in the clashes. Meanwhile, a senior PA official told The Jerusalem Post Abbas might meet with Olmert as early as next week. He added that Palestinian negotiators were also expected to meet with their Israeli counterparts in the coming days. Israeli and Palestinian officials are expected to meet this weekend US Gen. William Fraser, the envoy appointed by Secretary of State Condoleezza Rice to monitor both sides' implementation of the road map. Sources in Jerusalem said Israel was bracing for a report by Fraser that would take Israel to task for not dismantling settlement outposts set up since March 2001 and not freezing settlement expansion, as called for by the road map. Fraser was also expected to score the Palestinians for not implementing their road map obligations, foremost dismantling their terrorist capabilities and infrastructure. Abbas suspended talks with Israel in protest against the IDF operation in the Gaza Strip two weeks ago. Then, he said he would not resume the talks unless a cease-fire was announced between the Palestinians and Israel. The change in Abbas's position follows reports about an Egyptian-brokered truce that was allegedly reached recently between the Palestinians and Israel. Abbas declared Monday that Hamas and Israel had reached an agreement in principle on a truce. Both Olmert and Defense Minister Ehud Barak have said that no agreement was reached, and that Israel was not negotiating with Hamas either directly or indirectly. The official said Abbas had also come under heavy pressure from the US to resume the peace talks with Israel. "The Americans have been pressing him very hard," he said. "They don't want Hamas and other radical groups to sabotage the peace process." Hamas said the Egyptians were trying to arrange a cease-fire between the Islamist movement and Israel. Hamas legislator Mushir al-Masri said the PA in Ramallah was not involved in the efforts to reach a cease-fire. "The truce will be between the Palestinian resistance groups and Israel," he said. "Mahmoud Abbas has nothing to do with these efforts." Masri denied reports in the Arab media according to which Hamas and Israel had agreed on a 30-day period of calm, or tahdiyah, as a first step toward a full cease-fire. "There is no such thing as a trial tahdiyah," he said. "We insist on a comprehensive and mutual cease-fire." The Hamas official lashed out at Abbas for saying that Hamas had agreed to a cease-fire with Israel out of fear for the lives of its leaders. Abbas and other PA officials have mocked Hamas for reportedly agreeing to a truce. "Hamas is not begging for a cease-fire," Masri said. "Abbas and his authority in Ramallah have become mediators between the Palestinians and the occupation. They are a security agency for Israel." Another senior Hamas official, Khalil Abu Laylah, did not rule out reaching a truce with Israel. He, too, said Egypt was working toward achieving calm. "The Egyptians are hoping to achieve more than a truce," he said. "They are now talking about a package that would include the opening of the Rafah border crossing and other security-related issues." He insisted there were no direct contacts between Hamas and Israel. "The Egyptians are holding separate talks with all the parties," he said. "Once they achieve positive results, they will inform us. Then we will consider the offer." Abu Laylah dismissed Abbas's claim that Hamas and Israel had already agreed on a truce. "What Abbas declared is baseless," he said. "Abbas is trying to divert attention. Yaakov Katz contributed to this report.