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.

Israel's anti-aircraft defences went into action Saturday after a barrage of rocket fire from Gaza following the funeral of Islamic Jihad military commander Iyad al-Hassani, who was killed in an Israel strike the previous day, AFP reporters said.

Two men in their 40s were seriously wounded by rocket shrapnel in Sdot Negev, a cluster of Israeli communities not far from the Gaza border, emergency services said.

Islamic Jihad said its fighters were pursuing "missile strikes on Israeli cities" in revenge for Israeli "assassinations" of their commanders and strikes on populated areas.

Residents in the crowded Gaza Strip cowered indoors as the fighting raged, with streets empty and only a few shops and pharmacies open.

"I don't see any truce," Muhammad Muhanna, 58, told AFP in the ruins of his home. "The whole Palestinian people are suffering. What have we done?"

In Deir al-Balah in the central Gaza Strip, a dead donkey lay in the ruins of a row of buildings levelled in an Israeli strike.

"No one is safe in their homes," said Imad Rayan, 64.

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.

Palestinian prime minister Mohammed Shtayyeh "demanded UN intervention to stop Israeli crimes against our people in the Gaza Strip and the West Bank," his office said.

- 'Honourable agreement' -

The current bout of violence erupted on Tuesday when Israeli 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 Palestinian lives lost in the fighting, according to Gaza's health ministry, including children.

There has been one death inside Israel: an elderly woman who rescue services said was killed on Thursday night when a rocket struck the central city of Rehovot.

On Saturday, sirens warning of incoming fire sounded throughout the day in Israeli communities close to the border with Gaza.

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

A Palestinian source said Friday that Gaza factions were studying a new Egyptian ceasefire formula, while Israeli public television said an "improved" truce offer had been handed to Israel.

There had been cautious optimism a truce may be nearing, but an Islamic Jihad source 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".

Islamic Jihad said it had been seeking "an honourable agreement that reflects the interests of the Palestinian people and the resistance".

- Civilian lives -

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

The army said nearly 1,100 rockets had been fired from Gaza towards Israel in the current fighting, including 300 intercepted by its air defences.

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

Gaza, a coastal enclave that is home to 2.3 million Palestinians, has been plagued by poverty and unemployment since Israel imposed a blockade in 2007 when the Islamist movement Hamas took control.

The territory has seen numerous wars between militant groups and Israel since the Hamas takeover.

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