Palestinian media said between five and seven militants were killed in the air attack.
Israeli military officials declined to provide any figures, and denied Palestinian reports that the militants had managed to break into the Israeli Army base, located on the eastern border of the Palestinian enclave.
Al-Quds Brigades, the armed wing of the Palestinian Islamist organization Palestinian Islamic Jihad, and al-Aqsa Martyrs' Brigades, a Palestinian militant group closely linked to the Fatah political party, claimed responsibility for the attempted operation.
"This operation is a warning to the enemy, showing what is in store for it should it try to occupy the Gaza Strip. The enemy must know that it will have to pay dearly for that," a spokesman for the al-Quds Brigades said on Al-Aqsa TV.
The Israeli Army killed at least three Palestinian militants and wounded six in clashes in the Gaza Strip, local television reported earlier Thursday.
The Al Aqsa television channel said that the dead and wounded belonged to an armed Hamas faction, the Izzeddin al-Qassam Brigade.
Palestinian militants have been firing homemade Qassam rockets into Israel for the past week, and Israel has threatened to retaliate by cutting off electricity, water, and fuel supplies to the enclave.
A Wednesday meeting of the Israeli Cabinet reportedly decided against any major military incursion into Gaza for the time being, however Palestinian sources said Thursday that Israeli military personnel crossed into Gaza Wednesday night, and were continuing to conduct clearing operations near the town of Han Yunis.
