A new ceasefire proposal was circulated late Friday by Egypt, which has been mediating between the two sides, after a previous bid fell through, a Palestinian source said.

But the move did little to quell the fighting, and on Saturday morning witnesses in Gaza reported that air strikes pounded uninhabited areas of the crowded enclave, while air raid sirens wailed in neighbouring parts of Israel.

The exchange of fire came after the Palestinian health ministry reported the death of two men aged 19 and 32 in an Israeli army raid on a refugee camp in the occupied West Bank city of Nablus.

The Israeli army said it was a "counterterrorism" operation targeting operatives who had been planning attacks on soldiers.

"Armed gunmen fired at the forces, who responded with riot dispersal means and live fire," it said. "Two of the terrorists were targeted."

The Fatah movement of Palestinian president Mahmud Abbas said the two men killed in the raid were members of its armed wing, the Al-Aqsa Martyrs Brigades.

The current bout of violence erupted on Tuesday when Israeli air strikes on Gaza killed three leading Islamic Jihad members. Three other senior figures from the Palestinian militant group were killed in later strikes.

They are among at least 33 Palestinians killed in the fighting, according to Gaza's health ministry, including children.

A rocket killed an elderly woman in the central Israeli city of Rehovot, rescue services said.

- New ceasefire formula -

Egypt, a historic mediator between Israel and Gaza's factions, has been working on bringing and end to the fighting, the worst in the Israeli-Palestinian conflict since an August flare-up that killed nearly 50 Palestinians.

A Palestinian source on Friday said Gaza factions were studying Cairo's new ceasefire formula, adding that Egypt was also waiting for Israel's response.

Israeli public television meanwhile said an "improved" Egyptian ceasefire proposal had been handed to Israel.

Earlier, there had been cautious optimism that a truce may be nearing, with an Islamic Jihad source saying a deal drawn up by Cairo had been circulated among the group's leadership.

But the source subsequently said Israel was "disrupting Egypt's efforts for a ceasefire".

The United States, which along with the European Union has blacklisted Islamic Jihad and Hamas as terrorist groups, urged steps be "taken to ensure that violence is reduced".

US Deputy Secretary of State Wendy Sherman, in a call to Israeli Minister of Strategic Affairs Ron Dermer, "stressed the urgency of reaching a ceasefire agreement in order to prevent any further loss of civilian life", the State Department said.

An Islamic Jihad source said Mohammad al-Hindi, who heads the group's political bureau, arrived in Cairo on Thursday for talks with Egyptian intelligence officials.

He told AFP the group had been seeking "an honourable agreement that reflects the interests of the Palestinian people and the resistance".

- 'Honourable agreement' -

Morocco, which normalised relations with Israel in 2020, said it "firmly condemns recent Israeli attacks on the Gaza Strip, which have left numerous casualties among innocent civilians", a foreign ministry source said.

According to the Israeli army, in the latest flare-up more than 1,000 rockets have been fired from Gaza towards Israeli territory, including 300 that were intercepted by the Iron Dome defence system.

Israelis living in areas bordering the Palestinian territory have been told to stay close to bomb shelters.

Gaza, a coastal enclave with a population of about 2.3 Palestinians, has been plagued by poverty and unemployment since a blockade imposed by Israel in 2007 when the Islamist movement Hamas took over.

The territory has since been the site of numerous wars between militant groups and Israel, including the fighting in August in which 19 children were among the 49 killed, according to the United Nations.

Islamic Jihad fired over 1,000 rockets at Israel at the time, injuring three people.

The conflict has escalated since veteran leader Benjamin Netanyahu returned to power late last year, heading a coalition with extreme right and ultra-Orthodox parties.

Israel has also been shaken by its biggest domestic political crisis in decades, as mass protests have flared against plans to reform the justice system that have been spearheaded by Netanyahu, who is also battling corruption charges in court.