Israeli forces killed seven armed Palestinians in Gaza on Thursday, the military said, clamping down in an attempt to stop daily rocket fire, but a rocket from Gaza exploded near a school, terrifying children.

Palestinians confirmed three dead and 20 wounded in a day of fighting that involved Israeli airstrikes and ground operations. Earlier this week, a series of Israeli airstrikes killed 12 Gaza militants, including two top commanders of Islamic Jihad. Israel rejected a Hamas truce feeler, and defense officials said they were watching to see if the rocket fire would wind down to gauge the seriousness of the approach.

In amateur video of the rocket attack on the battered Israeli town of Sderot, taken from inside the school, the sound of the explosion is clearly heard. Children scream and cry as a teacher tries to round them up and guide them to a safe location. No one was hurt, but Israeli officials said about a dozen children suffered panic attacks, and one was taken to a hospital for treatment of shock.

Pictures like that from Sderot, a favorite target of rocket squads just a kilometer (half a mile) from the Gaza-Israel fence, have increased pressure on Israel's government to take action to stop the rocket attacks. Israeli Defense Minister Ehud Barak has said repeatedly that a large-scale invasion of Gaza is nearing, but experts and officials admit that such invasions have not stopped the rocket attacks in the past.

Instead, the military is using pinpoint strikes to try to deter the militants, like the separate clashes on Thursday.

Israeli forces in central Gaza killed two approaching gunmen Thursday morning, the army said, and later shot dead two more militants. Palestinians said two militants were killed.

Hospital officials said a third person was killed in the clash. His identity was not immediately known.

Reuters soundman Nihad Odehtallah was shot in the leg while covering the clashes and was taken to an Israeli hospital. His wounds were not life-threatening, and it was not clear whether Odehtallah was wounded by Israeli or Palestinian fire, the London-based news agency said. A photographer for Hamas television was also slightly wounded.

Israeli infantry and armored troops were in the area conducting a routine operation against militants who fire rockets and mortar rounds, try to infiltrate into Israel and plant bombs along the border fence, the military said.

Palestinian gunmen launched mortars at troops and fired at Israeli aircraft with machine guns as Israeli snipers took up positions on the roofs of homes in the area, witnesses said.

In the afternoon, the military said militants fired an anti-tank weapon, seriously wounding a soldier. The Israelis fired back, killing a Palestinian. Later, Israeli ground and air forces clashed with militants, and two were killed, the military said.

Palestinians said in that incident, a missile fired by an Israeli aircraft hit a house. Two people were apparently killed, they said, but ambulances could not approach the area.

Israel vowed to press ahead with its military operations.

"Israel will continue with its efforts to stop these rocket attacks and prevent the same type of tragedy that nearly occurred today," said Israeli government spokesman David Baker, referring to the rocket that exploded near the school.

Gaza militants fire rockets and mortar shells daily into southern Israel, severely disrupting life there. The projectiles have killed 12 people in six years.

Thursday's violence came a day after Israel's government rejected a feeler from Hamas for a truce to stop rocket fire from Gaza in return for a halt to Israeli military operations. Defense officials said they knew of no contacts with Hamas. Instead, they were looking for signs on the ground that Hamas was serious about a cease-fire — like a reduction in rocket salvos.

Vice Premier Haim Ramon said Thursday the overture was proof that Israel's strategy of blockading Gaza and battling militants there is working.

"All of these ... comments, and the messages coming in all kinds of strange ways, all of these things are a kind of smoke screen that just shows that Israel's recent policy toward Palestinian terror is bearing fruit," Ramon told Army Radio. If Palestinians stopped firing rockets into Israel, Israel would have no reason to attack, Ramon said.