Islamic Jihad commander among eight killed in explosion in refugee camp on Friday.
Hamas said the battles began around 1am after Israeli undercover units infiltrated houses east of the town of Rafah.
Tanks and bulldozers moved across the Israeli border into Gaza to back the troops, and Israeli aircraft struck twice, Hamas said.
The bulldozers were razing farmlands in an effort to deny rocket squads cover, and the army was carrying out arrest sweeps of men under 45, Hamas security and residents said.
According to Hamas, at least 25 men were arrested.
Moaiya Hassanain of the Gaza health ministry said nine men from the Hamas and Islamic Jihad groups were wounded by Israeli army fire and in the air raids.
Separately, a Hamas member wounded during an Israeli operation in Khan Younis three days ago, died of his wounds, the group announced.