The IDF will escalate the pace of its operations in the Gaza Strip - without penetrating more than three kilometers inside - defense officials said Wednesday night, after three soldiers were killed in a Hamas ambush in the morning opposite Kibbutz Be'eri. In response to the attack, the air force carried out a series of strikes throughout Gaza, killing close to 20 Palestinians and wounding dozens more. Over 20 Kassam rockets were fired into Israel throughout the day. The fighting on Wednesday broke a relative lull in violence in Gaza since the IDF's last broad offensive there in early March. The IDF operations in Gaza began late Tuesday night when troops from the Givati Brigade, backed by tanks from Brigade 401, swept into northern and southern Gaza in search of terrorist infrastructure. One soldier was moderately wounded overnight. On Wednesday morning, three soldiers - Sgt. Matan Ovdati, 19, from Moshav Patish; Sgt. Menhash Albaniat, 20, a tracker from an unrecognized village near Kuseife, in the Negev; and Sgt. David Papian, 21, from Tel Aviv - were killed in a Hamas ambush inside northern Gaza, opposite the fields of Kibbutz Be'eri. The troops were part of a 12-soldier unit that raided Gaza after two Palestinians were spotted moving toward the security fence to plant a bomb. The men came under heavy machine gunfire from a second Hamas force deployed on a nearby hill. Two of the soldiers were killed immediately, and the third sustained serious wounds; he died later at Soroka Medical Center in Beersheba. Two of their comrades were moderately wounded. "This is a continuous war, and our enemy - even after 60 years - does not accept the fact that we are here to stay," Defense Minister Ehud Barak said at a Labor Party meeting in the evening. "We will find a solution for the Kassams... it won't happen tomorrow or the next day, but we will bring the solution." The assessment in the defense establishment on Wednesday night was that the political echelon would not order a large incursion into Gaza, despite the casualties. Officials said that Pessah, next month's visit by US President George W. Bush and the celebrations for the state's 60th anniversary were all reasons that a large operation, even if deemed necessary, would need to wait a few months. Officials said the IDF would continue to operate in a defensive mode along the border with Gaza and within a 1-3 kilometer depth inside the Strip in an effort to prevent Hamas from fortifying its border positions, some of which it used to in Wednesday's attack. "Since Hamas stopped its rocket attacks there has been an increase in attacks along the border," a top officer in the Southern Command said. "They are now closer to the border than they used to be and that is the challenge." In the evening, an IAF helicopter fired four missiles at targets near the el-Bureij refugee camp in central Gaza. At least 12 Palestinians, including two youths, were killed, said Dr. Moaiya Hassanain of the Palestinian Health Ministry. Fadal Shana, a cameraman with Reuters, was killed along with two bystanders by an air strike in the same area, according to his colleagues and medics. Earlier, Palestinians reported six people killed in clashes with the IDF in Gaza. Four gunmen were killed and three were wounded in exchanges of fire in southern Gaza and an Islamic Jihad commander was killed when the motorcycle he was riding in the Jabalya refugee camp was hit from the air. In Gaza City, a spokesman for Hamas's armed wing, Izzadin Kassam, said two Hamas cells totaling eight gunmen took part in the ambush of the Givati soldiers. The spokesman, Abu Obaidah, said one of the cells managed to move toward the border while the second one lay behind in ambush. He said the first cell's mission was to attract the attention of the soldiers so that they would move straight into the ambush. The spokesman said the operation had been given the name "Field of Death" and that it would be followed by similar attacks soon. All the Hamas gunmen returned to their bases safely, he said. Defiant Hamas officials warned that the movement would step up its attacks against Israel in response to the continued blockade of the Gaza Strip and the Israeli military strikes that followed the ambush. Sami Abu Zuhri, a spokesman for Hamas, said Israel would "pay a heavy price for its ongoing crimes against our people." "We call on members of Izaddin Kassam to strike against the enemy everywhere," he said. "We must teach Israel an unforgettable lesson and avenge the killings of our people." Another Hamas official, Fawzi Barhoum, condemned the Arab countries for failing to act to end the blockade on the Gaza Strip. The Arabs were part of a conspiracy designed to bring the Palestinians to their knees, he said. The Hamas government in the Gaza Strip held the Palestinian Authority leadership responsible for the upsurge in IDF operations. "Some Palestinian officials in Ramallah have been encouraging the occupation to perpetrate massacres against our people," it said. Gil Hoffman and AP contributed to this report.