The Associated Press described the incident as Israeli tanks and bulldozers rolling into the eastern part of the city.
In the exchange of fire, the soldiers identified hitting two people, the army spokesman said.
"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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The agency also said an air strike killed an Islamic Jihad faction leader in his car.
The Al-Quds Brigades, Islamic Jihad's armed wing, said Raid Faanuna, one of its local leaders, was killed in an air strike "during a mission" east of Gaza City.
Diaa Abu Dhakar, another Al-Quds Brigades fighter, was killed during clashes with Israeli soldiers in Khan Yunis, - where seven more Palestinians were wounded as clashes flared.
Meanwhile, Reuters said forces clashed with Islamic Jihad fighters near the town on Wednesday, killing one Palestinian and wounding four.
Reuters also reported that three more Palestinian fighters died of shrapnel wounds near Gaza City.
One of them belonged to the armed wing of Hamas, which took control of Gaza earlier this month after routing forces loyal to Mahmoud Abbas, the Palestinian president and leader of the Fatah movement.
Israel pulled its forces and settlers out of the Gaza Strip in 2005, but has not stopped air strikes and other attacks against armed groups.
Representatives of the Quartet of Middle East mediators - the United States, the European Union, Russia and the United Nation - met in Jerusalem on Tuesday for talks aimed at boosting progress in talks between Israel and the Palestinian Authority following Hamas's Gaza takeover.