JERUSALEM (Reuters) -- Israel killed a man in the southern Gaza Strip 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.

Palestinian medics said the remains of Ghalib Irmeilat, 21, were taken to hospital, and another person was seriously wounded in an airstrike on a motorcycle in southern Rafah, near Gaza's frontier with the Egyptian Sinai.

Israel's military named the man wounded as Muhammad Rashdan, and said he was a member of Salafi group Tawhid and Jihad in Gaza.

An army statement said Rashdan and Irmeilat were involved in a raid on Monday from adjacent Sinai territory on the Israeli border, which killed a Palestinian citizen of Israel.

During the Sinai raid, soldiers shot dead two attackers, 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.

Israeli airstrikes killed four men in northern Gaza on Monday and two teenagers were killed by Israeli shelling on Tuesday morning.

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."

Egyptian ambassador to the Palestinian Authority Yasser Othman told Ma'an on Wednesday that Egypt was in touch with all parties in order to restore calm.

Ma'an staff contributed to this report