According to the radio station, the militant groups - Islamic Jihad and Al Aqsa Martyrs' Brigades, a violent wing of President Mahmoud Abbas's movement Fatah - claim to have killed one Israeli soldier, and taken another hostage.
The militants said one of their fighters remained on the Israeli side to fight the troops, while three returned to Gaza.
Israel's Armed Forces confirmed the attack, and said their troops had killed one of the Palestinian fighters at the checkpoint, near the Kissufim crossing. The army said they had suffered no casualties.
An Israeli-Palestinian ceasefire brokered on November 26 was breached in mid-May, when Palestinian militants launched rocket attacks on southern Israel, killing two people. More than 50 Palestinians have since been killed in Israeli retaliatory air attacks on Gaza.
The rocket attacks against Israel came amid factional fighting between Hamas and pro-presidential Fatah groups.
The border raid was the first time militants have successfully broken through the border since the kidnapping of two Israeli soldiers one year ago.
