Prime Minister Benjamin Netanyahu warned that nearly a week of fierce bombardment was "just the beginning" as Israel seeks to retaliate against Hamas after their surprise attack nearly a week ago.
Israeli ground forces made "localised" raids into Gaza in the last 24 hours "to cleanse the area of terrorists and weaponry" and try to find "missing persons", the army said.
At least 1,900 Gazans -- most of them civilians and including more than 600 children -- have been killed in waves of indisrminanate missile strikes on the densely populated enclave, the Palestinian health ministry said.
Israel has cut off water, fuel, and food supplies making a humanitarian crisis imminent in the small strip.
UN Secretary-General Antonio Guterres described the situation as having reached "a dangerous new low".
"We need immediate humanitarian access throughout Gaza," he added.
US President Joe Biden said addressing the humanitarian crisis was a "priority".
Tensions rose across the Middle East and beyond, with angry protests in support of the Palestinians, while Israel faced the prospect of a separate confrontation with Hezbollah in Lebanon.
A Reuters video journalist was killed in south Lebanon, the international news agency said. Two other Reuters reporters were injured, as were two from AFP and two from Al Jazeera.
In the occupied West Bank, at least 16 Palestinians were killed in clashes with Israeli forces during protests supporting Gaza, the health ministry said.
Thousands also demonstrated on Friday in Beirut, Iraq, Iran, Jordan and Bahrain in support of the Palestinians.
Palestinian Prime Minister Mohammad Shtayyeh accused Israel of committing "genocide" in Gaza.
But Netanyahu's spokeswoman Tal Heinrich told AFP: "Everything that happens in Gaza is Hamas's responsibility."
In Gaza, UN officials said the Israeli military, whose troops are massing at the border, had told them the evacuation should be carried out "within the next 24 hours".
It later admitted it would take more time, however, and did not confirm it had set the deadline.
But the world body described the immediate movement of some 1.1 million people -- nearly half of the 2.4 million in the Gaza Strip -- as "impossible".
"Forcing population transfers constitutes a crime against humanity, and collective punishment is prohibited under international humanitarian law," said Paula Gaviria Betancur, a UN expert on displacement.
She said it was "inconceivable" that so many Gazans would be able to cross an active war zone without "devastating humanitarian consequences".
The UN and others have urgently appealed for the mass evacuation order to be rescinded.
Hospitals are struggling to cope with the dead and wounded from the relentless bombardment, and the health system was "at a breaking point", the World Health Organization said.
In Jordan, after a meeting with US Secretary of State Antony Blinken, King Abdullah II called for "humanitarian corridors" to be opened urgently.
"Where to go?" asked Umm Hossam, 29, who was among the thousands fleeing.
"How long will the strikes and death last? We have no homes left, every area of Gaza is under threat," she added, her face streaked with tears.
AFP correspondents in Gaza said the Israeli military on Friday dropped flyers warning residents to flee "immediately" south of Wadi Gaza, with a map pointing south across a line in the centre of the 40 kilometre-long (25 mile-long) territory.
The army said it "will continue to operate significantly in Gaza City and make extensive efforts to avoid harming civilians".
"Hamas terrorists are hiding in Gaza City inside tunnels underneath houses and inside buildings populated with innocent civilians."
AFP correspondents said there were "heavy strikes" in the northern Gaza Strip on Friday, including on Al-Shati refugee camp and Gaza City, primarily targeting residential buildings.
The Hamas media office also reported Israeli air raids on Khan Yunis and Rafah in the south.
The Israeli military said its "fighter jets struck 750 military targets in the northern Gaza Strip overnight" including "residences of senior terrorist operatives used as military command centres".
Netanyahu, who was in security talks at military headquarters on Friday, has vowed to "crush" Hamas, and has likened it to the Islamic State group.
But in Geneva, the International Committee of the Red Cross said the unjustifiable "horrific" attacks on Israel could equally not justify "the limitless destruction of Gaza".
Israel also denied claims from rights groups that it has used the incendiary weapon white phosphorus, which can cause serious burns if it hits people.
Hamas has said Palestinians rejected the evacuation request, yet thousands of Gazans were on the move in search of safety, carrying plastic bags of belongings, suitcases on their shoulders and children in their arms.
Some walked while others drove, with belongings strapped to their trucks, cars and carts pulled by donkeys.
More than 423,000 people have already fled their homes, according to the UN, which said the evacuation order could turn what is "already a tragedy into a calamitous situation".
Gaza has been under a land, air and sea blockade since 2006 and Israel has vowed not to turn back on water, food and power supplies until all hostages are freed.
Arab League chief Ahmed Abul Gheit said Israel's evacuation order is a "forced transfer" that constitutes "a crime".
Palestinian president Mahmud Abbas said it will be "tantamount to a second Nakba" or "catastrophe", referring to the 760,000 Palestinians who fled or were expelled from their homes during the 1948 war that accompanied Israel's creation.
Russian President Vladimir Putin said that Israel risked waging an "unacceptable" siege in Gaza comparable to the Nazi blockade of Leningrad during World War II.
"We understand what that entails. In my opinion, this is unacceptable. More than two million people live there," he told journalists on a visit to Kyrgyzstan.
Israel has called up 300,000 reservists while forces, tanks and heavy weapons have been moved to the southern desert area around Gaza, an AFP correspondent reported.
Israeli soldiers have swept the southern towns and kibbutz farming communities since Saturday.
Israel faces a potential second front in the north after the Iran-backed Hezbollah group in Lebanon said it was "fully prepared" to join Hamas in the war when the time was right.
There has been cross-border fire in recent days, sparking concern about regional stability and prompting the United States to send additional munitions and its largest aircraft carrier.
President Biden has warned other regional powers not to get involved.
Israel's arch foe Iran has long financially and militarily backed Hamas and praised its attack, but insists it was not involved.