The armed wing of the governing Hamas movement and the Popular
Resistance Committees said in a joint statement they carried out an ambush, killing an Israeli officer and wounding several other soldiers.
"I can confirm that an Israel Defence Forces non-commissioned officer was killed by gunfire," an army spokesman said. "(Soldiers) were fired upon in central Gaza ... during an operation to eliminate terrorist infrastructure."
Israeli troops and settlers quit the Gaza Strip a year ago but the army launched a ground offensive in the area after Palestinian gunmen seized a soldier in a cross-border raid on June 25. He is still being held.
More than 210 Palestinians, about half of them civilians, have been killed in Israeli operations against militants over the past three months.
Describing the latest violence, witnesses said gunmen had exchanged fire with Israeli soldiers in an area of central Gaza after troops backed by tanks had moved across the border just after dawn.
Israeli airstrike
The clash came one day after Palestinian factions agreed to form a unity government to try to end Western sanctions imposed on the Hamas-led administration for refusing to recognise Israel and renounce violence.
Israel has responded sceptically to the unity government while the Hamas Islamist movement has said it would never recognise Israel.
Earlier, an Israeli air strike destroyed the two-storey central Gaza home of a senior security official in the Interior Ministry, witnesses said. No one was wounded.
An Israeli army spokesman said the house was targeted because it was being used to store weapons.
In addition to serving in the Interior Ministry, the official whose home was targeted is a member of Hamas.