Israel's missile attacks on the densely populated Palestinian enclave killed a top Islamic Jihad commander and left a crater in a seven-storey office building that Israel's military said was used by Gaza's Islamist rulers Hamas.
"The directive is to continue to strike at terror targets," Prime Minister Benjamin Netanyahu said after a meeting with military chiefs. "We will continue to act as necessary to restore peace and security to all residents of Israel."
The armed wing of Hamas promised more rockets in return: “The criminal Zionist enemy intensified its bombing of homes and residential apartments in the recent hours, and therefore, we warn the enemy that if it did not stop that immediately, we would resume rocketing Tel Aviv,” said spokesman Abu Ubaida.
US President Joe Biden, in a call with Netanyahu later on Monday, expressed his support for a ceasefire in the fighting, the White House said in a statement.
"The President expressed his support for a ceasefire and discussed US engagement with Egypt and other partners towards that end," it said.
Rocket barrages, some of them launched in response to the killing of Islamic Jihad's Hussam Abu Harbeed, sent Israelis dashing for bomb shelters. A synagogue was hit in Ashkelon and an apartment building in Ashdod.
Gaza health officials put the Palestinian death toll since hostilities flared up last week at least 212, including 61 children and 36 women. Ten people have been killed in Israel, including two children.
The Israeli military said militants had fired about 3,350 rockets from Gaza, and that Israeli air and artillery strikes had killed least 130 Palestinian combatants.
With the fiercest regional hostilities in years showing no sign of abating, US Secretary of State Antony Blinken urged all sides to protect civilians.
Late on Monday Hamas denied that it had offices in the building, known as al-Jala: "These are false allegations and an attempt to justify the crime of targeting a civilian tower," Hamas spokesman Fawzi Barhoum said in a statement.
Blinken and other US officials put in calls to Egypt, Jordan and the United Arab Emirates on Monday, and a US envoy to the region met Palestinian President Mahmoud Abbas.
Egypt and UN mediators also stepped up diplomatic efforts, while the UN General Assembly will meet to discuss the violence on Thursday.
Despite the flurry of US mediation, the US administration approved the potential sale of $US735 million in precision-guided weapons to Israel, and Congressional sources said on Monday that US lawmakers were not expected to object to the deal.
ISLAMIC JIHAD
As Islamic Jihad mourned Harbeed's death, Israel's military said he had been "behind several anti-tank missile terror attacks against Israeli civilians". An Israeli general said the country could carry on the fight "forever".
At least seven Palestinians were killed in Israeli strikes on Gaza on Monday by evening. Two died in the missile attack on the office building, which Israel's military said was used by Hamas internal security.
"My children couldn't sleep all night even after the wave of intensive bombing stopped," said Umm Naeem, 50, a mother of five, as she shopped for bread in Gaza City.
Earlier on Monday, Israel bombed what its military called 15 km (nine miles) of underground tunnels used by Hamas. Nine residences belonging to high-ranking Hamas commanders in Gaza were also hit, it said.
"We have to continue the war until there is long-term ceasefire - (one) that is not temporary," Osher Bugam, a resident of the Israel coastal city of Ashkelon, said after a rocket fired from Gaza hit the synagogue there.
Medics said seven people were injured in the rocket strike that hit the apartment building in Ashdod.
COMMUNAL VIOLENCE
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.
Palestinians have also become frustrated by setbacks to their aspirations for an independent state and an end to Israeli occupation in recent years.
World concern 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.
The hostilities between Israel and Hamas-controlled Gaza have been accompanied by an uptick of violence in the West Bank, where the Palestinians have limited self-rule. Alarmingly for Israelis, there have also been riots involving both Arab and Jewish mobs within Israel itself, and clashes in towns populated both by Jews and members of Israel's 21% Arab minority.
Police said an Israeli man died in hospital on Monday after being attacked by Arab rioters last week.
Israel's president has warned that tension between Jewish and Arab Israelis could devolve into "civil war".
General strikes are planned for Tuesday in Arab towns within Israel and Palestinian towns in the West Bank, with posts on social media urging solidarity "from the sea to the river."
While the devastation in Gaza was likely to make it harder for Israel to expand its ties with Arab countries, Gulf states that opened ties with Israel last year are showing no public sign of second thoughts.