Israeli Prime Minister Benjamin Netanyahu said the country is "embarking on a long and difficult war" as it deals with an unprecedented hostage crisis after Palestinian militants launched a surprise land, sea and air attack from Gaza Saturday, killing hundreds and infiltrating into Israeli territory.

The shock attacks by Hamas led to the deadliest day in decades for Israel and come after months of surging violence between Palestinians and Israelis with the decades-long conflict now heading into uncharted and dangerous new territory.

Israel's political-security cabinet convened late Saturday and made a "series of operational decisions aimed at bringing about the destruction of the military and governmental capabilities of Hamas and the Palestinian Authority, in a way that would negate their ability and desire to threaten and harm the citizens of Israel for many years to come," according to a statement from the office of Israel's Prime Minister.

Netanyahu vowed "mighty vengeance" on the Palestinian militant group Hamas following its unprecedented assault on Israel that appeared to catch the entire Israeli military and intelligence apparatus off guard in one of the country's worst security failures.

Throughout Saturday and into Sunday, Hamas launched thousands of rockets from the Gaza Strip into Israel -- making direct hits on multiple locations inside the country including Tel Aviv -- while armed terror groups entered Israel and infiltrated military bases, towns and farms, shooting at civilians and taking hostages.

At least 300 Israelis have been killed, an Israeli official told CNN and more than 1,500 have been injured, Israeli media reported.

Israel responded by launching air strikes on what it said were Hamas targets in Gaza, while its forces clashed on the ground with Hamas fighters in villages, army bases and border crossings.

Israeli warplanes continued to pound Gaza on Sunday morning with the Israel Defense Forces saying it had struck 426 targets in Gaza, including 10 towers used by Hamas.

In Gaza, at least 232 Palestinians have died and more than 1,600 are wounded, the Palestinian health ministry said.

The Israeli leader said the "first phase" of the operation had ended with the "destruction of the majority of the enemy forces that penetrated our territory."

Netanyahu announced Israeli forces have started an "offensive formation" which will "continue without reservation and without respite until the objectives are achieved." Among the decisions made by the cabinet is to stop the supply of electricity, fuel and goods to Gaza.

Complicating Israel's response is that a "significant number" of Israeli nationals were taken by Hamas as hostages and are being held at locations across Gaza.

"It is unprecedented in our history that we have so many Israeli nationals in the hands of a terrorist organization," Israeli Defense Forces spokesman Lt. Col. Jonathan Conricus (Res) told CNN, without giving an exact number. "I can assure you that the IDF will be focused on getting each and every Israeli back."

"These are numbers that we have never, ever seen before," he added.

It has been more than 17 years since an Israeli soldier was taken as a prisoner of war in an assault on Israeli territory. And Israel has not seen this kind of infiltration of military bases, towns and kibbutzim since town-by-town fighting in the 1948 war of independence.

In a statement Saturday, Palestinian militant group Hamas said the captured Israeli hostages are being held across Gaza and warned against attacks in the area.

"Threatening Gaza and its people is a losing game and a broken record," said Abu Obaida spokesman for the Al Qassam Brigades, the armed wing of Hamas in a recorded audio message late Saturday. "What happens to the people of the Gaza Strip will happen to them and beware of miscalculation."

Earlier the group claimed to have captured "dozens" of Israelis, including soldiers, and were holding them in "safe places and resistance tunnels."

The IDF said Sunday that "many hundreds," possibly as many as 1,000 Hamas fighters were involved in the attack, according to Conricus, who said fighting inside Israel was still ongoing as of 4.15 a.m. local time Sunday morning (9.15pET on Saturday).

The priority for the Israeli military Sunday was to "make sure that we clear all Israel communities of terrorists that are still inside Israel," he said, adding that the IDF was still "clearing the last houses and locations and communities and bases."

"Hopefully, at the break of dawn we will be able to declare that we have finally restored sovereignty and order in Israel. But that has not yet been achieved. And that will be our number one priority," he said.

'No warning of any kind'

Saturday's attack prompted strong reactions from around the world. US President Joe Biden said his administration's support of Israel's security is "rock solid and unwavering" and many European leaders denounced the violence, while Brazil said it will call an emergency meeting of the United Nations Security Council.

Air France said it is suspending its flights to Tel Aviv and US aviation officials issued a special bulletin to pilots and airlines urging "extreme caution."

The highly coordinated assault, which began Saturday morning, was unprecedented in its scale and scope and came on the 50th anniversary of the 1973 War in which Arab states blitzed Israel on Yom Kippur, the holiest day of the Jewish calendar.

"We had no warning of any kind, and it was a total surprise that the war broke out this morning," Efraim Halevy, the former head of Mossad, Israel's Intelligence Service, told CNN.

The number of rockets fired by Palestinian militants was at a scale "never seen before," Halevy said, and this was "the first time" that Gaza has been able to "penetrate deep into Israel and to take control of villages."

"This is beyond imagination from our point of view, and we didn't know they had this quantity of [rockets], and we certainly didn't expect that they would be as effective as they were today," he said.

Fighting carried on throughout the day and into the night, and a fresh round of rocket attacks hit Tecl Aviv and other areas on Saturday evening. The IDF urged civilians in Gaza to leave their residential areas as Israeli military operations continued.

Air raid sirens and rockets could be heard in Israel throughout the night into Sunday.

"You can hear the intercept missiles banging in the air," said CNN's International Diplomatic Editor Nic Robertson as he arrived at Ben Gurion Airport in Israel.

It is rare for Palestinian militants to be able to make it into Israel from Gaza which is sealed off and heavily watched by Israel's military. Gaza is one of the most densely packed places in the world, an isolated coastal enclave of almost 2 million people crammed into 140 square miles.

Governed by Hamas, the territory is largely cut off from the rest of the world by an Israeli blockade of Gaza's land, air and sea dating back to 2007. Egypt controls Gaza's southern border crossing, Rafah. Israel has placed heavy restrictions on the freedom of civilian movement and controls the importation of basic goods into the narrow coastal strip.

Fighting between the two sides has surged in the last two years.

The violence has been driven by frequent Israeli military raids in Palestinian towns and cities, which Israel has said are a necessary response to a rising number of attacks by Palestinian militants on Israelis.

They also come at a moment of deep division in Israel, months after the country's right-wing government pushed through a contentious plan to reduce the power of the country's courts, sparking a social and political crisis.

Pleas for release of hostages

Israelis are sharing photos of friends and family who they say have been kidnapped by Hamas militants and are urging the public to help spread the word in hopes of getting them back safely.

Yoni Asher, a resident of Sharon region, told CNN he recognized his wife from a viral video that shows a group of people loaded into the back of a truck flanked by Hamas militants.

Asher said his wife and young daughters were visiting his mother-in-law in Nir Oz, a kibbutz near the Gaza border. He said he contacted them on Saturday morning and suspected they may have been abducted. He tracked his wife's phone and learned that it was located in Gaza, he said.

Later that day, he saw the viral clip. In the video, a woman is seen in the truck as a militant puts a scarf on her head. Asher told CNN that the woman is his wife though CNN has not been able to independently verify the video.

"The situation is not looking good," Asher said, adding that his wife and mother-in-law have German citizenship and pleaded with the German government for help.

A German foreign ministry source told CNN that, "the Federal Foreign Office and the German embassy in Tel Aviv are in close contact with the Israeli authorities in order to clarify whether and to what extent German citizens are affected."

An Israel Police spokesperson has told CNN that family members who wish to report their loved ones as missing to come to the nearest police station when it's safe to leave their homes. The police suggested relatives bring photos and personal items from which DNA samples can be extracted to help with identification.