Hamas said two Palestinians were injured, one, a fighter, seriously.
The movement said that its fighters later fired two rocket-propelled grenade launchers at an army bulldozer, setting it on fire. The army said no damage was caused.
Rocket fire from the Gaza Strip into Israel persisted during the operation.
Islamic Jihad said it fired one rocket toward the southern Israeli town of Sderot but no injuries were immediately reported.
Israeli troops frequently enter the Gaza Strip to conduct operations against rocket launching squads and destroy tunnels used to smuggle weapons.
Soldiers have conducted several such incursions since Hamas took control of the coastal area in the middle of June.
Israel evacuated army bases and nearly 9,000 Jewish settlers from the Gaza Strip almost two years ago.