Israeli sources said the aircraft struck targets including an office building of the mainstream Fatah faction and another in a refugee camp in central Gaza.
Witnesses at the camp said it destroyed an office of the Popular Front for the Liberation of Palestine.
A third Israeli missile struck an office of the Popular Resistance Committees in the Gaza suburb of Tel al-Hawa, the sources said.
An Israeli aircraft fired a missile at a target in the northern Gaza Strip early on Wednesday, destroying a bridge, Palestinian security officials said.
The army said the airstrike in Bait Hanun targeted a road leading to an area used by Palestinian fighters to fire rockets.
There were no reports of casualties in any of the raids but rescue workers continued to sift through rubble in the darkened streets.
West Bank raids
Israeli troops also swept into two West Bank towns before dawn on Wednesday in a raid on offices of Hamas and Islamic Jihad fighters, witnesses said.
Israeli forces raided two West
Bank towns early on Wednesday
Witnesses said 15 army vehicles had stopped outside offices of both groups in the central West Bank town of Tulkarim where troops launched searches and confiscated equipment.
More than two dozen other army vehicles raided the offices of Islamic charities suspected of aiding Hamas in the town of Qalqilya, south of Tulkarim, witnesses said.
The latest offensive began just two hours after Israel launched artillery fire on Gaza late on Tuesday.
"Our artillery fired several rounds at an uninhabited sector of the Gaza Strip from which a Qassam rocket was fired at our territory," an Israeli military spokeswoman said on Tuesday night, speaking of the use of artillery on Gaza for the first time since it was occupied in 1967.
No casualties were reported in either incident.
Earlier on Tuesday, Israel fired more missiles into the Gaza Strip and its warplanes buzzed the Gaza Strip, breaking the sound barrier twice and frightening people, an AFP journalist reported.
After air strikes destroyed two bridges and two buildings Israel said were used by fighters, Defence Minister Shaul Mofaz said armed groups would "be hit again and again until they understand there are new rules to the game".
He did not rule out an incursion back into Gaza or artillery fire and said Israel could assassinate political leaders of the biggest group Hamas just as it killed Shaikh Ahmed Yassin and Abdel Aziz al-Rantissi in 2004.
"Quiet means quiet," Mofaz was quoted by the YNET media website as saying.
"Until there is quiet, terrorist organisations will know no quiet. If [Hamas leaders] Mahmoud al-Zahar or Ismail Haniyah or others continue with rocket fire, we will send them to the same place as Rantissi and Yassin."
After Mofaz's remarks, a political leader of Islamic Jihad said it and other groups had decided at a meeting to abide again by an informal truce.
After a weekend volley of 40 rockets into Israel, Islamic Jihad's political leader Khaled al-Batsh said it and other groups had agreed at a meeting to "renew our commitment to calm while reserving the right to respond if Israel continued its attacks".
"If [Hamas leaders]Mahmoud al-Zahar or Ismail Haniyah or others continue with rocket fire, we will send them to the same place as Rantissi and Yassin"
Israeli defence minister
But afterwards, another Gaza rocket crashed into Israeli territory. However, it caused no injury or damage.
A statement from Islamic Jihad's armed wing claimed responsibility. But another Jihad spokesman denied this.
Meanwhile, Israeli troops rounded up 84 people in the West Bank, bringing to over 300 the number arrested since Sharon ordered a crackdown on armed factions last weekend.
Also on Tuesday, a forensic report published by the Palestinian Authority said shrapnel found in the bodies of people killed in a blast at a Hamas rally last week came from the group's own homemade rockets.
The report by the Interior Ministry's explosives unit said the shrapnel resembled that used in the noses of Hamas' Qassam rockets.
The blast at the rally in the crowded Jabaliya refugee camp on Friday killed 21 people, including a 7-year-old boy who died of his wounds on Tuesday.
The Jabaliya blast last week killed
21 Palestinians, including a boy
Hamas said Israeli aircraft had fired missiles into the crowd, but Israel denied this.
The Palestinian Authority said the blast happened when Hamas activists mishandled explosives during the celebration of Israel's withdrawal from Gaza.