Gaza militants said on Wednesday they were ready to sign up to an Egyptian-brokered truce to end three days of cross-border fighting after Israeli air strikes killed a Palestinian militant and a 14-year-old boy.

In a statement, the militant wing of the Islamist Hamas group in control of Gaza said: "Responding to the Egyptian efforts, we and the armed resistance announce our commitment to stop this round of confrontation as long as the occupation stops this aggression."

Israel had no immediate comment. It customarily avoids responding whenever intermediaries reach an accord with Gaza militants as Israel refuses to recognise them citing the Islamists' refusal to acknowledge Israel's existence.

The Israeli military had earlier said in a statement it would "continue to operate with perseverance and determination against those who use terror against the State of Israel".

An Egyptian source had earlier told Reuters that efforts were afoot to try to achieve a ceasefire in fighting seen as risking a wider conflict at a time when Egypt faces political uncertainty after a contested presidential election.

Monday's violence erupted after a cross-border attack launched from Egypt's Sinai desert killed an Israeli civilian. Israel shot dead two of the attackers, then launched air strikes on Gaza, killing eight, including Wednesday's victims.

A newly formed radical Islamist movement, the "Shura Council of Mujahideen in the Holy Land", claimed responsibility for Monday's raid from Egypt.

An Israeli raid on Wednesday killed a member of a fringe Islamist Salafi network Israel said was involved in Monday's violence. He was struck while riding his motorcycle in Rafah, near Gaza's border with Egypt, medical officials said.

A second air strike in Gaza City killed a 14-year-old boy and wounded his father, also a civilian, the officials said.

The Israeli military confirmed the air strikes, saying the second one had targeted a squad firing rockets from a largely civilian-inhabited area in northern Gaza.

Israel launched two more air strikes on Hamas security bases in Gaza after darkness fell, lightly injuring two Palestinian boys aged 13 and 14, who sustained shrapnel wounds, medics said. Israel confirmed these attacks as well.

Palestinians fired more than 50 rockets into Israel on Wednesday, sending panicky residents fleeing to safe rooms or shelters, and damaging a home but causing no casualties, police and the Israeli army said.

Cairo has brokered Gaza truces in the past, but they sometimes take days to evolve. An Egyptian official said an agreement by Israel and Palestinian factions had earlier been secured to cease hostilities on Tuesday night but had fallen through.