Barrages of rockets were fired from the blockaded Gaza Strip on Saturday, killing 200 people in Israel and at least 232 in Gaza.
Sirens blared across the country's south and central areas, with Israel authorities urging people to stay near bomb shelters.
The armed wing of the Palestinian terror group Hamas said it was behind the attack, claiming that it launched over 5,000 rockets at its neighbour.
"We decided to put an end to all the crimes of the occupation (Israel), their time for rampaging without being held accountable is over," the group said.
"We announce Operation Al-Aqsa Flood and we fired, in the first strike of 20 minutes, more than 5,000 rockets."
"Severe Hostage Situation" In Some Desert Communities: Israel Army
"There are still 22 locations where we are engaging with terrorists that came into Israel, from the sea, from the land and from the air," said army spokesman Richard Hecht on what he labelled a "robust ground invasion".
Hamas earlier released images of several Israelis taken captive, and another army spokesman, Daniel Hagari, confirmed that "there are kidnapped soldiers and civilians.
"I can't give figures about them at the moment. It's a war crime committed by Hamas and they will pay the price."
Mr Hecht said there was also a "severe hostage situation" in the Negev desert communities of Beeri and Ofakim east of Gaza.
The Israel death count from the Hamas surprise attack Saturday has surged to more than 200, the army said, accusing the Hamas of breaking into homes and "massacring civilians".
Israel Vows "Mighty Vengeance" After Deadliest Day For 50 Years
"We will take mighty vengeance for this black day," Prime Minister Benjamin Netanyahu said.
"Hamas launched a cruel and wicked war. We will win this war but the price is too heavy to bear," he said. "Hamas wants to murder us all. This is an enemy that murders mothers and children in their homes, in their beds. An enemy that abducts elderly, children, teenage girls," Benjamin Netanyahu said.
Israeli Troops Still Battling "Hundreds" Of Terrorists, Says Army
Israeli troops were still battling "hundreds" of Palestinian terrorists at 22 locations inside Israel Saturday after they infiltrated from Gaza during a massive dawn rocket barrage, the army said.
"There are still 22 locations where we are engaging with terrorists that came into Israel from the sea, from the land and from the air," army spokesman Richard Hecht told journalists, adding the Hamas attack included a "robust ground invasion".
Joe Biden Vows "Rock Solid" Support For Israel
President Joe Biden described the assault as "a terrible tragedy on a human level" and said he had spoken to Israeli Prime Minister Benjamin Netanyahu to underline his support.
"In my administration, support for Israel's security is rock solid and unwavering. We'll make sure that they have the help their citizens need and they can continue to defend themselves," President Biden said.
Biden stressed that Israel -- which the United States has supplied with billions of dollars of arms -- has "a right to defend itself and its people" after the terrorist group Hamas launched air, sea and land strikes.
Hamas Solely Responsible, Will Bear Results: Israel To UN Security Council On Attacks
Israel told the United Nations Security Council on Saturday that the Palestinian terror group Hamas "holds the sole responsibility and will bear the results" of its attack on the country.