GAZA, June 1 (Nidal al-Mughrabi/Reuters) - A Palestinian gunman broke into Israel on Friday and killed a soldier before being shot dead himself in a rare cross-border attack that Israel blamed on the Islamist group Hamas.

Israel hit back, with a missile-strike wounding three people in the southern Gaza Strip. Militants also fired rockets out of the Palestinian enclave, but they did not caused any damage, the Israeli army said.

Sources in Gaza said the dead gunman was affiliated with the Islamic Jihad. However, the faction, which operates independently of Hamas, denied responsibility, suggesting the infiltrator might have been acting alone.

Hamas, which governs Gaza, had no immediate comment on the incident.

The Israeli army said the gunman crossed through the border fence with the intention of killing civilians and had ambushed soldiers sent to intercept him.

Palestinian witnesses heard an explosion and shooting near Abassan, a border village that is also close to the Egyptian frontier shared by Israel. They said Israeli forces set off smoke bombs to obscure the view as helicopters circled.

Though hostile to Israel, Hamas has largely sat out recent cross-border fighting and has appeared unwilling to rock the boat. Rather, it is focused on power-sharing talks with its Palestinian rivals and is monitoring developments in Egypt.

The Hamas terror organization is solely responsible for any terrorist activity emanating from the Gaza Strip, the Israeli army said in a statement.

The flare-up in violence came the day after Israel gave Palestinian authorities the bodies of 91 militants, who were killed in various attacks on Israel in recent decades, saying it hoped the move would help restart frozen peace efforts.

The dead were hailed as fallen martyrs on their return to the West Bank and Gaza, their coffins draped in the Palestinian flag and given a heroes' welcome. (Reporting by Dan Williams and Nidal al-Mughrabi; Editing by Crispian Balmer)