The first attack hit offices of the Hamas-controlled Economy Ministry in Gaza City, setting the building on fire. Rescue teams rushed to the scene of the attack, located near a housing complex inhabited by about 600 people.
Later, an Israeli airstrike destroyed a small bridge near the Bureij refugee camp in central Gaza, the army said.
A separate airstrike on a Hamas rocket workshop in Gaza City killed one Palestinian and wounded seven people, Palestinian medics said. The medics had initially said two people were killed, but one turned out to be seriously wounded. The building was demolished in the attack and Palestinian rescue workers were searching through the rubble.
Israeli helicopters also opened fire on an area in northern Gaza where militants had gathered to fire rockets at southern Israel, killing an 18-year-old Bedouin, Khalil Abu Naghafieb, said hospital officials.
Israel has been waging an offensive in Gaza for more than two weeks since an Israel soldier was captured by Palestinian militants in a daring cross-border raid on an Israeli outpost. Israel has pledged to push forward, even while it battles Hezbollah guerrillas in Lebanon.
Ending the latest phase of the offensive in Gaza, the army said it pulled ground troops out of central parts of the territory on Friday, three days after moving into the area. However, the air campaign continued.
Israel has killed dozens of Palestinians, many of them gunmen, and repeatedly attacked government buildings linked to Hamas during the offensive. Israel has rejected demands that it release hundreds of Palestinian prisoners in exchange for the captured soldier, Cpl. Gilad Shalit, 19.
One Israeli soldier also has died during the offensive, accidentally shot by fellow troops.
On Thursday, an Israeli warplane bombed the Palestinian Foreign Ministry, collapsing part of the structure and causing widespread damage in the area.
It was Israel's second use of a huge bomb in Gaza City in as many days. At least 23 Palestinians were killed in Gaza on Wednesday, including nine who died when an Israeli F-16 warplane dropped a quarter-ton bomb on a house where militant leaders were secretly meeting.
The United States blocked an Arab-backed resolution on Thursday that would have demanded Israel halt its military offensive in the Gaza Strip, the first U.N. Security Council veto in nearly two years.
The draft, sponsored by Qatar on behalf of other Arab nations, accused Israel of a "disproportionate use of force" that endangered Palestinian civilians, and demanded Israel withdraw its troops from Gaza.
The United States was alone in voting against the resolution. Ten of the 15 Security Council nations voted in favor, while Britain, Denmark, Peru and Slovakia abstained.
By IBRAHIM BARZAK