The six soldiers were killed at a West Bank checkpoint, shot at close range by militiamen linked to Palestinian leader Yasser Arafat's Fatah movement.
CBS News Correspondent Robert Berger reports one missile landed near Yasser Arafat's office in Ramallah but he was not hurt.
It was the closest Israel has come to harming Arafat in nearly 17 months of bloodshed which U.S. and international mediation has failed to curb.
Learn more about the history of the Arab-Israeli conflict.
Arafat remained in his Ramallah office, the lights turned off and accompanied by a few close aides, said one of his advisers, Ahmed Abel Rahman. Under siege at his West Bank headquarters since early December, he emerged defiant.
"The tanks and the missiles and the planes do not terrify us," he told reporters. "The Israelis insist on avoiding the peace process but we will raise the Palestinian flag on the walls of Jerusalem."
Prime Minister Ariel Sharon is discussing further military action with his cabinet. Political sources say Sharon has decided on an even harsher response in days to come.
Sharon spokesman Raanan Gissin declined to specify what measures would be taken but said the overnight strikes in the West Bank and Gaza Strip "might be a small example of the kind of operations that would come to end the terror."
The ambush ignited debate on the military's tactics, including the effectiveness of checkpoints, and intensified pressure on Sharon to take more decisive action in stopping Palestinian attacks. "It's clear that the strategy that we've had until now can't continue," said the Israeli president, Moshe Katsav.
In all, 15 Palestinians were killed, according to Palestinian officials: four in a missile attack on Arafat's Gaza compound, seven in Israeli shelling of two Palestinian police checkpoints near the West Bank town of Nablus, two in a firefight outside the Balata refugee camp close to Nablus, one in an airstrike on a Palestinian police post in the town of Ramallah, and one in a firefight near Ramallah.
Twelve of the dead were Palestinian policemen.
Abdel Rahman said the Palestinians had a right to fight the Israeli occupation, implying support for the ambush on the Israeli soldiers.
"The Palestinian people have a legitimate right to resist, which will not stop without ending the occupation," Abdel Rahman said, adding that the Palestinian Authority remained opposed to attacks in Israel.
Israeli Foreign Ministry official Gideon Meir said Israel will retaliate for "this terror campaign which was imposed on us...by Yasser Arafat and his gang."
The past week has been one of the bloodiest since fighting began in September 2000. Fifteen Israelis were killed, including 11 soldiers, a policeman and three civilians. In the same period, 45 Palestinians were killed, including nine civilians, 22 members of the security forces and 12 assailants and suspected militants.
The ambush on the soldiers was carried out at about 9 p.m. Tuesday at an Israeli military checkpoint near the village of Ein Arik, west of Ramallah. The post was manned by eight soldiers who had arrived for a tour of duty just hours earlier. Israeli media reports said the Palestinian gunmen apparently were aware of the changeover.
Two or three gunmen approached the checkpoint from a dirt path and opened fire, taking the soldiers by surprise. Five soldiers were killed on the road and a sixth in a nearby trailer that served as shelter for the troops. Another soldier in the trailer was wounded. A soldier in a lookout position was unharmed, the reports said.
A Fatah leader in the West Bank, Marwan Barghouti, was quoted as saying that the ambush was one of the Palestinians' "most successful" operations. The Al Aqsa Brigades, a Fatah-affiliated militia, claimed responsibility.
Israeli military commentators sharply criticized the army's performance. "In the killing fields of the intefadeh (Arabic for Palestinian uprising), Israeli soldiers have gone from being the hunters to being hunted. Sitting ducks," wrote commentator Alex Fishman in the Yediot Ahronot daily.
In the Haaretz daily, commentator Zeev Schiff wrote that the incident raised serious questions "about the very existence of the checkpoints and about the need for an overall strategy."
Israeli reprisals began around 3 a.m. Wednesday.
In the Gaza Strip, Israeli F-16 warplanes bombed a four-story police compound, razing the building and sending debris and shrapnel flying in all directions.
Palestinians in nearby buildings fled in panic. Carrying her 9-month-old baby, with her 3-year-old son behind her, Ilham Johfur, 26, said: "This is another night of terror." Hundreds of people were in the streets, fearing their buildings would be hit.
In all, Palestinians counted at least 40 explosions in the Gaza raids.
In Ramallah in the West Bank, helicopter gunships fired a missile at a trailer serving as sleeping quarters for policemen in Arafat's compound. The officers had left the trailer in anticipation of an Israeli strike.
Elsewhere in Ramallah, a Palestinian policeman was killed in a missile attack on his post and a gunman died in a firefight with Israeli troops west of the city.
Near Nablus, Israeli troops fired heavy machine guns and tank shells at two Palestinian police posts, Palestinian security officials said. Six policemen were killed in one attack, and one was killed in a second strike.
South of Nablus, Israeli tanks moved close to the Balata refugee camp. Two Palestinians, a civilian and a gunman, were killed in a firefight, doctors said.