The Al-Quds Brigades, the armed wing of the Islamic Jihad, said Raid Faanuna, a local leader, was killed in an air strike "during a mission" east of Gaza City.
A 12-year-old boy and two men were killed in Gaza City by a shell fired by an Israeli tank, residents and medical workers said.
Fawzi Barhoum, a Hamas spokesman, said the Israeli incursion was part of a conspiracy to pressure Hamas. He accused Mahmoud Abbas, the Palestinian president, of being party to the conspiracy.
"The refusal by the US, EU et al to deal with Hamas reflects their disrespect for the wishes of the Palestinian people"
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Abbas, speaking in the West Bank city of Ramallah, condemned the Israeli raid and said:
"We strongly condemn these criminal acts, either in Gaza or the West Bank.
We are against violence in all its forms and also we are against launching rockets."
Witnesses in Khan Younis said they saw an Apache helicopter flying low and heard heavy shooting and periodic explosions as Israeli soldiers patrolled rooftops and Palestinian fighters ran through the streets.
Diaa Abu Dhakar, another Al-Quds Brigades fighter, was killed during clashes with Israeli soldiers in Khan Younis - where seven more Palestinians were wounded as clashes flared
Twenty Palestinians, including seven in critical condition, were taken to hospital in Gaza City.
In the south, two fighters form the Al-Quds Brigades and Hamas's armed Izz al-Din al-Qassam Brigades were killed in the fighting. Another two Palestinians were wounded.
The Israeli army said the activity was against "terror threats" in Gaza, where Hamas fighters overran security forces loyal to Abbas on June 15.
News agencies reported conflicting accounts of the attacks, recording a combination of land incursions and an air strike.
The Israeli army denied carrying out an air assault, but confirmed land offensives.
|Raid Faanuna, a leader of the Al-Quds Brigades, was found burnt in his car [Reuters]|
An Israeli army spokesman said: "There is activity in the northern Gaza Strip and the southern Gaza Strip, in the area of Gaza City and the area of Khan Younis."
Two Israeli soldiers were wounded by an anti-tank missile during the operations that Ephraim Sneh, Israel's deputy defence minister, described as "preventive measures" to foil rocket attacks from Gaza.
Source: Al Jazeera and agencies