Israel killed a Gaza militant on Wednesday as a surge of fighting across the border of the Palestinian enclave entered a third day despite what Egypt said were its efforts to broker a truce.

The militant, a Palestinian belonging to one of Gaza's fringe Islamist Salafi networks, died and a comrade was wounded in an air strike on their motorcycle in southern Rafah, near Gaza's frontier with the Egyptian Sinai, medical officials said.

Israel said the man targeted had been involved in a raid on Monday from adjacent Sinai territory into the Jewish state, which killed an Israeli. Soldiers shot dead two infiltrators, who were later claimed by a newly formed radical Islamist movement, the "Shura Council of Mujahideen in the Holy Land".

Palestinians fired at least 16 rockets into Israel on Wednesday, causing no casualties, the military said.

Fighters from Gaza's ruling Hamas movement have joined in the barrages after months of staying on the sidelines, a shift that holds the prospect of a wider conflict during the contested ascendancy for political Islam in Egypt.

Cairo has brokered Gaza truces in the past and an Egyptian official said renewed mediation had secured agreement by Israel and Palestinian factions on Tuesday night.

A Palestinian source accused the Israelis of violating the deal. Israel neither confirmed nor denied there was such deal, and the military said in a statement it would "continue to operate with perseverance and determination against those who use terror against the State of Israel".