The worst attack on Israel for decades unleashed a war that both sides vowed to escalate.
At least 200 Israelis were reported killed and 1100 wounded by gunbattles raging in more than 20 locations inside Israel.
In Gaza, health officials reported more than 230 people killed and 1600 wounded.
"Our enemy will pay a price the type of which it has never known," Israeli Prime Minister Benjamin Netanyahu said.
"We are in a war and we will win it".
Hamas says it fired a volley of 150 rockets towards the Israeli city of Tel Aviv.
Hamas leader Ismail Haniyeh said the assault that had begun in Gaza would spread to the West Bank and Jerusalem.
"This was the morning of defeat and humiliation upon our enemy, its soldiers and its settlers," he said in a speech.
"What happened reveals the greatness of our preparation. What happened today reveals the weakness of the enemy."
In Sderot, in southern Israel near Gaza, bodies of Israeli civilians lay strewn across a highway, surrounded by broken glass.
A woman and a man were sprawled out dead across the front seats of a car.
A military vehicle drove past the bodies of another woman and a man in a pool of blood behind another car.
"I went out, I saw loads of bodies of terrorists, civilians, cars shot up. A sea of bodies, inside Sderot along the road, other places, loads of bodies," said Shlomi from Sderot.
Terrified Israelis, barricaded into safe rooms, recounted their plight by phone on live TV.
"They just came in again, please send help," a woman identified as Dorin told Israel's N12 News from Nir Oz, a kibbutz near Gaza.
"My husband is holding the door closed... They are firing rounds of bullets."
In Gaza, black smoke and orange flames billowed into the evening sky from a high rise tower hit by an Israeli retaliatory strike.
Crowds of mourners carried the bodies of killed militants through the streets, wrapped in green Hamas flags.
Gaza's dead and wounded were carried into crumbling and overcrowded hospitals with severe shortages of medical supplies and equipment.
Streets were deserted apart from ambulances racing to the scenes of air strikes.
Israel cut the power, plunging the city into darkness.
Hamas said it fired a volley of 150 rockets towards Tel Aviv on Saturday evening in retaliation for an Israeli air strike that took down a high rise building with more than 100 apartments.
Hamas deputy chief Saleh al-Arouri told al-Jazeera that the group was holding a big number of Israeli captives, including senior officials.
He said Hamas had enough captives to make Israel free all Palestinians in its jails.
The Israeli military confirmed Israelis were being held in Gaza.
A military spokesman said Israel could mobilise up to hundreds of thousands of reservists and was also prepared for war on its northern front against Lebanon's Hezbollah group.
Hamas said the attack was driven by what it said were Israel's escalated attacks on Palestinians in the West Bank, Jerusalem and against Palestinians in Israeli prisons.
"This is the day of the greatest battle to end the last occupation on earth," Hamas military commander Mohammad Deif said, announcing the start of the operation in a broadcast on Hamas media and calling on Palestinians everywhere to fight.
The Israeli military has confirmed that Israelis are being held in Gaza.
In Gaza, a narrow strip where 2.3 million Palestinians have lived under an Israeli blockade for 16 years, residents rushed to buy supplies in anticipation of days of war ahead.
Some fled their homes and headed for shelters.
"We are afraid," Palestinian woman, Amal Abu Daqqa, told Reuters as she left her house in Khan Younis.
US President Joe Biden denounced the Palestinian attack and pledged support for Israel.
United Nations Middle East peace envoy Tor Wennesland condemned the attacks on Israel, warning in a statement: "This is a dangerous precipice, and I appeal to all to pull back from the brink."
