"Palestinian security forces are conducting an investigation and hunting down the terrorists parallel to investigations and operations conducted by the Israeli security forces," the official told Maariv newspaper.
Late Tuesday Hamas claimed responsibility for the killing of four Israelis, gunned down in a drive-by shooting near Kiryat Arba.
Commenting on the shooting, Israeli President Shimon Peres said Wednesday, "The terrorists will not triumph." Expressing his condolences to the families, the president said, "There should be no negotiations with terrorists, but we should hold talks with those that denounce terror and want peace," the Hebrew daily quoted him saying.
Defense Minister Ehud Barak said Israel's security forces will not rest until the perpetrators of the attack are caught, Israel Radio said.
Opposition leader Knesset member Tzipi Livni said Tuesday's attack was aimed at derailing efforts to achieve peace.
"We cannot let the terror attack interfere with our fulfillment in the negotiations for peace," The Jerusalem Post quoted her as saying.
Palestinian Authority Prime Minister Salam Fayyed condemned the attack, which he said counters the Palestinian interests.
"We condemn this operation, which runs counter to Palestinian interests and against efforts of Palestinian leadership to mobilize international support for the rights of our people as well as with previously signed agreements," Fayyed told the Ma'an news agency
On Wednesday the victims of the terrorist shooting were buried. All lived in Beit Hagai near Hebron.
Yitzhak, 47, and Talia Aimes, 45, were the parents of six children, ranging in age from 18 months to 24 years. Arutz Sheva, Israel's National News Web site said Talia was nine months pregnant.
Kochava Even-Chaim, 37, is survived by her husband and 8-year-old daughter. Her husband Maimon, a volunteer in the regional emergency response team, was one of the first to arrive at the scene following the shooting, and spotted his wife's body. Avishai Schindler, 24, is survived by his wife.