Israeli aircraft also fired a missile at a house in Khan Yunus used by money changers. An Israeli army source said the missiles hitting Bait Hanun targeted access routes that the Palestinian fighters used to fire rockets into Israel.
"Our aircraft attacked three bridges in the Bait Hanun sector, in the north of the Gaza Strip, which enabled terrorists to reach sectors from where it was possible to fire Qassam rockets at Israel," an Israeli army spokeswoman said.
No one was hurt in the pre-dawn strike on Bait Hanun.
Wail al-Dahduh, Aljazeera's correspondent, confirmed on Tuesday from Gaza that Israeli warplanes launched overnight air strikes targeting Khan Yunis in the southern Gaza Strip and Bait Hanun in the north.
Ready to resume
Israeli helicopters, warplanes and F-16 fighters are maintaining a steady presence over Gaza's skies, ready to resume attacks any time, he said.
So far, Israeli aircraft have strafed a Fatah office, damaging it and nearby residential buildings in a heavily populated area in khan Yunus, al-Dahduh said.
The southern Gaza town of Khan
Yunus has been repeatedly hit
The attacks also targeted two roads leading to Bait Hanun town in the northern Gaza Strip, he added. Those damaged by the air strikes include the main road linking Bait Hanun to Bait Lahia, Gaza city and other areas in Gaza Strip, and a road used by citizens to move from Gaza Strip to the West Bank.
Gaza is living in fear of the Israeli threats of continued assassinations and air strikes as part of its extended military operation in the recently vacated Palestinian territory, al-Dahduh added.
A Palestinian security official confirmed raids on Khan Yunus
and Bait Hanun.
"The attacks slightly wounded one person and caused major damage in a building used by money changers, and in another building used by Fatah," he said.
The worst surge of violence since Israel's Gaza pullout on 12 September after 38 years of occupation has tested a shaky truce.
Hamas' call to halt rocket attacks
has not placated Israel
Hamas called off its rocket launches after an Israeli air strike killed a military chief from Islamic Jihad on Sunday. But not all Palestinian factions have followed suit.
Hostilities first erupted when a blast on Friday killed 16 people at a Hamas rally in Gaza.
Hamas blamed Israel and its fighters fired at least 40 rockets into the Jewish state in response, wounding several people.
Israel denied responsibility and the Palestinian Authority said it appeared to be an accident caused by Hamas members carrying explosives.
Hamas claimed responsibility on Tuesday for taking captive and killing Sasson Nuriel, a 51-year-old Jerusalem man who was found dead on Monday.
Hamas said in a statement that they had seized Nuriel on Wednesday with the intention of trading him for Palestinian prisoners held in Israeli jails.
However, after Israel began a series of arrest raids against West Bank militants, they decided to kill him, the statement said.
Monday's Israeli offensive came hours after a senior member of the Islamic Jihad resistance group was killed by an Israeli air strike.
Muhammad Khalil was riding in a Mercedes along a coastal Gaza road when a missile fired from an Israeli aircraft killed him and his bodyguard.
Israel has been continuing with its air campaign despite a call by Hamas leader Mahmud al-Zahar to end the group's rocket attacks.
Al-Zahar spoke at a news conference late on Sunday, saying his group remained committed to a seven-month-old cease-fire and that he wanted to prevent further Israeli attacks.