One of gunmen was killed in an air strike on north Gaza and three others were wounded. All of the fighters belonged to Islamist group Hamas, which controls the enclave, and were guarding the border, the reports said.
Another fighter, a field commander of the al-Aqsa Martyrs Brigade, a paramilitary group affiliated to Fatah, was shot by Israeli soldiers in the West Bank.
Seven Palestinians including a mother and child were killed in Israeli air strikes on Gaza on Thursday. The fighting escalated on Tuesday when an Israeli raid on Gaza killed 19 people. A total of 34 Palestinians have been killed by Israeli troops in the past three days.
Gaza militants fired at least six rockets into Israeli territory on Thursday, slightly injuring an Israeli woman, the Israeli military said.