US President Joe Biden called for a "significant de-escalation" in Israel's conflict with Gaza's armed groups ahead of a diplomatic push Thursday to stem the violence, as the sides traded further fire.
Israeli fighter jets hit the residences of at least six Hamas leaders, according to an army statement, which said "military infrastructure" was stored at each site.
As air raid sirens sounded again early Thursday in southern Israel, the second most powerful group in Gaza, Islamic Jihad, claimed credit for a fresh volley of rockets.
The persistent unrest came after a strong call from Washington on Wednesday for an easing of the hostilities that erupted on May 10.
"The president conveyed to the prime minister (Benjamin Netanyahu) that he expected a significant de-escalation today on the path to a ceasefire," the White House said after a fourth phone call in a little over a week.
Germany's top diplomat was due for talks in Israel on Thursday, in the latest effort to broker a ceasefire.
Over 10 days, Israeli strikes have killed 227 Palestinians, according to the Gaza health ministry, while Palestinian rocket fire has claimed 12 lives in Israel, according to Israeli police.
An Israeli military official, speaking on condition of anonymity, said Israel was assessing at what stage it may stop its military campaign.
"We are looking at when is the right moment for a ceasefire," said the source.
Netanyahu earlier issued a tough threat against Hamas, who Israel says is responsible for the estimated 4,000 rockets fired at the Jewish state since May 10.
"You can either conquer them, and that's always an open possibility, or you can deter them, and we are engaged right now in forceful deterrence," Netanyahu told foreign ambassadors.
"But I have to say we don't rule out anything."
Speaking later, the hawkish premier said: "I am determined to continue this operation until its objective is achieved: to restore quiet and security" for Israelis.
Hamas chief Ismail Haniyeh said the group that has run Gaza since 2007 could "continue its resistance longer than the occupation (Israel) estimates."
- Sitting in a wheelchair -
Among those killed in Israeli bombardment in Gaza on Wednesday were a disabled man, his pregnant wife and their three-year-old child, the health ministry in the enclave said.
The family's living room was blasted to bits, and the mangled parts of a child's red bicycle lay amid the wreckage.
Omar Saleha, 31, whose brother Eyad was killed in the strike, said the family was having lunch when their home was hit.
"What did my brother do? He was just sitting in his wheelchair," Saleha told AFP.
- Diplomatic flurry -
The US, a key Israel ally, has repeatedly blocked adoption of a joint UN Security Council statement calling for a halt to hostilities.
France proposed a ceasefire resolution on Tuesday, which earned initial support from China.
But the US said Wednesday it would not support the proposed resolution, saying it could undermine efforts to de-escalate the crisis.
German Foreign Minister Heiko Maas was to meet Israel's foreign and defence ministers on Thursday and travel to the occupied West Bank for talks with the Palestinian Authority.
- Humanitarian crisis -
The Hamas rocket barrages have prompted many living in communities near the Gaza border to hide in bomb shelters virtually around the clock.
The dead on the Israeli side include one child, one Indian and two Thai nationals, with 333 wounded, Israeli authorities said.
Gaza's death toll counts 64 children, and 1,620 injured, according to health ministry figures.
Israel's bombing campaign has also left the two million population in Gaza, under Israeli blockade for 14 years, desperate for relief.
Hospitals have been overwhelmed, and some 75,000 civilians have fled their homes, seeking refuge in UN-run schools and other public buildings, the United Nations says.
The International Committee of the Red Cross on Wednesday said that people in both Gaza and Israel "urgently need respite from non-stop hostilities".
"People in Gaza - exhausted from sleepless nights, from constant fear, worry and grief - need a window during which they can go outside and about their business without fear of being killed or injured, or of witnessing death," Fabrizio Carboni, ICRC director for the Near and Middle East, said in a statement.
- West Bank deaths -
The latest escalation was sparked after clashes broke out at Israeli-annexed east Jerusalem's flashpoint Al-Aqsa mosque compound, one of Islam's holiest sites.
This followed violence over the attempted evictions of Palestinian families from homes in the eastern sector's Sheikh Jarrah district.
The conflict has since sparked mob violence between Jews and Israeli Arabs, and sharply heightened tensions in the occupied West Bank.
The Palestinian health ministry said a Palestinian woman was shot dead Wednesday near Hebron, as the army said she had tried to attack Israeli forces.
The death brought to 25 the number of Palestinians killed in the West Bank since May 10.
In northern Israel, the army said it fired artillery shells toward southern Lebanon, in response to four rockets launched at the Jewish state from Lebanese territory, in the third such attack in less than a week.