The UN Security Council was due to meet Sunday after Israeli air strikes on the Gaza Strip killed eight children and demolished a building housing media offices, sparking international outcry.
c, the sixth day of bombardments on the Palestinian enclave controlled by Islamist group Hamas, which fired back rocket barrages.
One strike on Gaza killed 10 members of an extended family.
The children "didn't carry weapons, they didn't fire rockets", said Mohammad al-Hadidi, one of the grieving fathers.
At least 159 people, mostly Palestinians, have been killed since the cross-border fire began last week.
The UN Security Council was due to meet Sunday to discuss the bloodiest conflict between the Jewish state and Palestinian militants since 2014.
UN Secretary-General Antonio Guterres was "dismayed" by civilian casualties in Gaza and "deeply disturbed" by Israel's strike on the tower housing news bureaus, a spokesperson said Saturday.
Guterres "reminds all sides that any indiscriminate targeting of civilian and media structures violates international law and must be avoided at all costs", he said.
Israel ally Washington, which blocked a UNSC meeting scheduled for Friday, has been criticised for not doing enough to stem the bloodshed.
US Secretary for Israel-Palestinian Affairs Hady Amr was to hold talks Sunday with Israeli leaders before meeting Palestinian officials to seek a "sustainable calm", the State Department said.
US President Joe Biden again underscored Israel's right to defend itself in a phone call with Israeli Prime Minister Benjamin Netanyahu.
Biden also expressed his "grave concern" over the violence as well as for the safety of journalists.
In a televised statement late Saturday, Netanyahu thanked Biden for "unequivocal support".
Netanyahu told the US that Israel did its utmost to safeguard civilians in its Gaza bombing campaign.
"The proof is that towers containing terror sites are cleared of uninvolved people prior to being attacked," he said.
Mohammed al-Hadidi said he had lost most of his family in a strike on a three-storey building in the Shati refugee camp that killed 10 relatives -- two mothers and their four children each. Israel's army claimed the building was used by senior Hamas officials.
"They are striking our children -- children -- without prior warning," said the devastated father, whose five-month-old baby was also wounded in the explosion.
Palestinian militants responded with volleys of rockets into Israel, killing a man on the outskirts of commercial capital Tel Aviv, police and medics said.
Balls of flame and a mushroom cloud of debris shot into the sky Saturday afternoon as Israel's air force flattened the 13-floor Gaza building housing Qatar-based Al Jazeera and the Associated Press news agency, after giving a warning to evacuate.
"It is clear that those who are waging this war do not only want to spread destruction and death in Gaza, but also to silence media that are witnessing, documenting and reporting the truth," Al Jazeera's Jerusalem bureau chief, Walid al-Omari, told AFP.
AP President and CEO Gary Pruitt said he was "shocked and horrified" by the attack.
Jawad Mehdi, the owner of the Jala Tower, said an Israeli intelligence officer had told him he had just an hour to evacuate the building.
Israeli defence officials said the building housed not only news bureaus but offices of Hamas militants.
AFP Chair Fabrice Fries said the agency "stands in solidarity with all the media whose offices were destroyed in Gaza" and called on all parties "to respect the media's freedom to report on events".
Israel continued to pound Gaza through the night, damaging another building of around a dozen floors and killing at least two. Around 30 others were wounded in western Gaza.
Earlier in the day, Biden also spoke to Palestinian president Mahmud Abbas in their first call since the US president took office.
Israeli air and artillery strikes on Gaza since Monday have killed 147 people including 41 children, and wounded another 1,100.
Palestinian armed groups have fired at least 2,300 rockets at Israel, killing 10 people, including a child and a soldier, and wounding over 560 Israelis. Israeli air defences have intercepted many rockets.
Palestinians on Saturday marked the Nakba, the "catastrophe" that saw hundreds of thousands of Palestinians displaced during Israel's creation in 1947-1948.
Two Palestinians were killed in clashes with Israeli forces Saturday in the West Bank, the day after some of the worst clashes in recent years in the territory left 11 Palestinians dead.
A Palestinian security source said the fighting was the "most intense" since the second intifada, or uprising, that began in 2000.
Also Read | Biden, Netanyahu discuss Gaza after media strike
Pro-Palestinian demonstrators staged protests across the world, including in Paris, where police used water cannon against them.
Israel is also trying to contain Jewish-Arab violence within its borders.
Major clashes broke out at the Al-Aqsa mosque compound -- Islam's third-holist site -- on May 7 following a crackdown against protests over planned Israeli expulsions of Palestinians in the Sheikh Jarrah neighbourhood of Israeli-occupied east Jerusalem.
At a protest in the district Saturday, an AFP journalist saw Israeli forces beating a woman inside a car and shoving a young female protester to the ground.
Some 10,000 Gazans have fled homes near the Israeli border for fear of a ground offensive, the UN said.
"They are sheltering in schools, mosques and other places during a global Covid-19 pandemic with limited access to water, food, hygiene and health services," UN humanitarian official Lynn Hastings said.
Mixed Jewish-Arab towns within Israel have also seen mob violence, with more than 750 people arrested this week, police said.
Israel's northern borders with Lebanon and Syria, with which it remains technically at war, were also tense.
Three rockets were launched from Syria Friday, while Israel's army said it fired "warning shots" towards potential infiltrators from Lebanon, killing a Lebanese protester.