Calling the IDF action in Gaza a "war," Prime Minister Ehud Olmert warned Tuesday that Israel will continue to hunt down all terrorists involved in rocket attacks against Israeli communities in the western Negev. The IDF went on high alert across the country on Tuesday ahead of predictions that Islamic Jihad would escalate its attempts to perpetrate a terrorist attack inside Israel in response to a series of air strikes that started Monday and have killed 13 Palestinians. Despite the threat, defense officials said Israel would continue to target terrorists involved in rocket attacks against Sderot. "We will continue to chase after the terror chiefs and will hit them," Olmert said during a meeting of his Kadima faction. "We will get to every single person involved in rocket attacks against Israel." "This is not a unilateral war," he said. "The defense establishment has made great achievements in the past two days with its daring operations in this war against terror chiefs in Gaza. This war will not stop." The IDF air strikes began Monday night with the targeted killing of Majed Harazin, Islamic Jihad's leader in the Gaza Strip. In another air strike early Tuesday, the IDF killed Karim al-Dahdouh, a master rocket-maker. At 6 a.m. Tuesday, the IDF killed another four members of Islamic Jihad's Al-Quds Brigades in the northern Gaza Strip. The IDF said their terrorist cell was involved in Kassam rocket attacks. Later in the day, two Hamas operatives were killed when an IAF aircraft bombed a Hamas military position in southern Gaza. The IDF said the bombing was in response to mortar fire on Kerem Shalom. The Quds Brigades' commander in Jenin, Tarik Abu-Ra'ali, was killed during an exchange of fire with troops in Kabatiya, south of Jenin, Palestinians reported. The IDF said Palestinian gunmen had fired at the soldiers, who returned fire. The IDF did not confirm that Ra'ali had been killed. Defense Minister Ehud Barak told US Special Envoy for Middle East Security James Jones on Tuesday that Israel must take precautions and be on the alert for a possible response by Islamic Jihad to the recent air strikes. Barak told Jones that Israel "must hope that the IDF successes [in Gaza] continue to prevent rocket attacks against the western Negev." Islamic Jihad's spokesman in the Gaza Strip, Abu Hamza, hinted that his organization would carry out suicide attacks in Jewish towns in the Gaza periphery in retaliation for the air strikes. "We have a long arm," he said on Hamas television. "You will soon [experience] strikes similar to those we carried out in Tel Aviv, Netanya and Eilat." Abu Hamza warned that Islamic Jihad would step up Kassam attacks on Sderot, Ashkelon, Yad Mordechai and Netivot. Earlier, in an e-mail sent to reporters, Islamic Jihad said it would retaliate for its losses with suicide attacks inside Israel, threatening "a wave of martyrdom operations." Hamas leader Ismail Haniyeh told a Channel 2 reporter Tuesday he was prepared to negotiate an end to the rocket attacks and Israeli attacks, a Hamas spokesman told Israel Radio. Vice Premier Haim Ramon praised the military action and said the operations "greatly impeded" the terrorist groups' activities. He predicted the air strikes would result in a decrease in rocket attacks. Deputy Defense Minister Matan Vilna'i said he was "very pleased with our achievements [Monday] night ," but added that the air strikes were not an alternative to a ground operation. Gil Hoffman contributed to the report.