Hours after the air strike, around 30 Israeli tanks penetrated two kilometres into Gaza, between the southern towns of Rafah and Khan Younis, witnesses said.
The Israeli spokeswoman said a "regular operation" was under way in the area.
Witnesses said Israeli troops cut traffic on Gaza's main north-south road and exchanged fire with Palestinian fighters.
Three members of the Islamic Jihad group were killed by a tank shell, witnesses and Palestinian medics said.
Soldiers took over the rooftops of several homes and detained about 60 people in house-to-house raids, residents said.
The Israeli military said they were detained for questioning.
In the major West Bank city of Nablus, a Palestinian fighter died when an explosive he was planning to use against Israeli troops detonated accidentally, local residents said.
The spokeswoman said Israeli troops had made two arrests during a raid in Nablus and that the fighter died while he was preparing a bomb to use against the force.
Hospital officials identified the dead man as a member of the al-Aqsa Martyrs' Brigades, an offshoot of the Fatah movement led by Mahmoud Abbas, the Palestinian president.
They said three other people were wounded by the explosion.
Troops often raid West Bank towns and villages looking for members of armed groups suspected of involvement in attacks against Israelis.
The violence came a day after Ehud Olmert, Israel's prime minister, pledged to "forge a historic path" towards a final accord with the Palestinians in the first formal peace talks in seven years.
He warned that if Israel tries to maintain control over Palestinian territories, its future as a Jewish state is in jeopardy.
Olmert told a business conference on Monday that the stakes are high for Israel.
Answering critics who reject concessions to the Palestinians, Olmert said creation of a Palestinian state next to Israel is vital.
The talks are set to open Wednesday.