Israel bombed what it said were underground tunnels used by Hamas and Palestinian fighters fired rocket barrages at Israeli cities as fighting spilled into a second week on Monday amid mounting international calls for a ceasefire.

There was no sign of any imminent end to the most serious hostilities in years between Israel and the Hamas Islamists who rule Gaza, where 2 million Palestinians live.

The sound of explosions roared overnight as dozens of Israeli fighter jets bombed what the military said was an underground tunnel system used by Hamas. Witnesses said roads, security buildings and fighters training camps had been attacked in and around Gaza City.

After Gaza rockets were fired at the Israeli cities of Beersheba and Ashkelon, Israeli aircraft struck nine residences belonging to high-ranking Hamas commanders, the military said. Some of the homes were used for weapons storage, it said.

Later in the morning, Palestinian media reported that Israel had struck a factory in northern Gaza. Video on social media showed a column of thick black smoke rising into the air.

There were no reports of casualties on either side of the border.

World concern had already deepened after an Israeli air strike in Gaza that destroyed several homes on Sunday and which Palestinian health officials said killed 42 people, including 10 children, and persistent rocket attacks on Israeli towns.

Injecting more urgency into Washington's calls for calm, U.S. Secretary of State Antony Blinken wrote on Twitter: "All parties need to deescalate tensions - the violence must end immediately", after he spoke with Egypt's foreign minister about ongoing violence in Israel, Gaza and the occupied West Bank.

At a U.N. Security Council meeting on Sunday, the United States said it had made clear to Israel, the Palestinians and others that it was ready to offer support "should the parties seek a ceasefire".

Prime Minister Benjamin Netanyahu said Israel's campaign in Gaza was continuing at "full force", and that deterrence had to be achieved to prevent future conflict with Hamas.

"We are acting now, for as long as necessary, to restore calm and quiet to you, Israel's citizens. It will take time," Netanyahu said in a televised address after his security Cabinet met on Sunday.

The Gaza Health Ministry put the death toll since the hostilities flared at 197, including 58 children and 34 women. Ten people have been killed in Israel, including two children, Israeli authorities say.

Hamas began its rocket assault last Monday after weeks of tensions over a court case to evict several Palestinian families in East Jerusalem, and in retaliation for Israeli police clashes with Palestinians near the city's Al-Aqsa Mosque, Islam's third holiest site, during the Muslim holy month of Ramadan.

SUSTAINED CALM

U.S. President Joe Biden said his administration is working with all parties towards achieving a sustained calm.

"We also believe Palestinians and Israelis equally deserve to live in safety and security and enjoy equal measure of freedom, prosperity and democracy," he said in a pretaped video aired at an event marking the Muslim Eid holiday on Sunday.

In New York, U.N. Secretary-General Antonio Guterres told the Security Council that the United Nations was "actively engaging all sides toward an immediate ceasefire" and urged them "to allow mediation efforts to intensify and succeed." U.N. envoys have helped to mediate past truces between Israel and Hamas.

Washington, a strong ally of Israel, has been isolated at the United Nations over its objection to a public statement by the Security Council on the violence because it worries it could harm behind-the-scenes diplomacy.

Jordan's King Abdullah said his kingdom was involved in intensive diplomacy to halt the bloodshed, but did not elaborate.

The Israeli military said that Hamas, a group regarded by Israel, the United States and the European Union as a terrorist movement, and other armed factions have fired more than 2,800 rockets from Gaza over the past week.

An Israeli anti-missile system intercepted many of the rockets, while some fell short of the border.

Hamas said its attacks were in retaliation for Israel's "ongoing aggression against civilians", including the air strike in Gaza City on Sunday that destroyed a number of homes.

The Israeli military said civilian casualties were unintentional and that its jets attacked a tunnel system used by militants, which collapsed, bringing the homes down. Hamas called it "pre-meditated killing".

On U.S. network CBS' "Face the Nation" programme, Netanyahu defended another Israeli air strike a day earlier that destroyed a 12-storey building where the Associated Press and the Al Jazeera TV network had offices.

He said the structure also housed the militant group's intelligence office, making it a legitimate target. He said Israel had passed information about the building to U.S. authorities. A U.S. intelligence official did not respond to a request for comment.

Israel had given advance warning to occupants to leave. The Associated Press has condemned the strike and called on Israel to present evidence that Hamas was in the building.