Tel Aviv. Israeli soldiers battled Hamas fighters in the streets of southern Israel on Sunday and launched retaliation strikes that leveled buildings in Gaza, while in northern Israel a brief exchange of strikes with Lebanon's Hezbollah militant group raised fears of a broader conflict.

There was still some fighting underway more than 24 hours after an unprecedented surprise attack from Gaza, in which Hamas militants, backed by a volley of thousands of rockets, broke through Israel's security barrier and rampaged through nearby communities. At least 600 people have reportedly been killed in Israel -- a staggering toll on a scale the country has not experienced in decades -- and more than 300 have been killed in Gaza.

The militants also took captives back into the coastal Gaza enclave, including women, children and the elderly, whom they will likely try to trade for thousands of Palestinian prisoners held by Israel. Secretary of State Antony Blinken told CNN's "State of the Union" that the US is working to verify reports that “several” Americans were killed or are missing.

The high death toll, multiple captives and slow response to the onslaught pointed to a major intelligence failure and undermined the long-held perception that Israel has eyes and ears everywhere in the small, densely populated territory it has controlled for decades.

Israeli Prime Minister Benjamin Netanyahu said the country was at war and would exact a heavy price from its enemies. His Security Cabinet officially declared the country at war in an announcement on Sunday, saying the decision formally authorizes “the taking of significant military steps."

The implications of the announcement were not immediately clear. Israel has carried out major military campaigns over the past four decades in Lebanon and Gaza that it portrayed as wars, but without a formal declaration.

Yohanan Plesner, the head of the Israel Democracy Institute, a local think tank, said the decision is largely symbolic, but "demonstrates that the government thinks we are entering a more lengthy, intense and significant period of war.”

A major question now was whether Israel will launch a ground assault into Gaza, a move that in the past has brought intensified casualties. Netanyahu vowed that Hamas “will pay an unprecedented price.” But, he warned, “This war will take time. It will be difficult.”

Civilians paid a staggering cost for the violence on both sides. Several Israeli media outlets, citing rescue service officials, said at least 600 people were killed in Israel, including 44 soldiers, while officials in Gaza said 313 people had died in the territory. Some 2,000 people have been wounded on each side. An Israeli official said security forces have killed 400 militants and captured dozens more.

Israeli TV news aired a stream of accounts from the relatives of captive or missing Israelis, who wailed and begged for assistance amid a fog of uncertainty surrounding the fate of their loved ones. In Gaza, residents fled homes near the border to escape Israeli strikes, fleeing deeper inside the territory after warnings in Arabic from the Israeli military.

In neighboring Egypt, a policeman shot dead two Israeli tourists and an Egyptian at a tourist site in Alexandria, the Interior Ministry said. Egypt made peace with Israel decades ago, but anti-Israel sentiment runs high in the country, especially during bouts of Israeli-Palestinian violence.

The flare-up on Israel's northern border also threatened to draw into the battle Hezbollah, a fierce enemy of Israel's which is backed by Iran and estimated to have tens of thousands of rockets at its disposal. Hezbollah fired dozens of rockets and shells on Sunday at three Israeli positions in a disputed area along the border and Israel’s military fired back using armed drones. Two children were lightly wounded by broken glass on the Lebanese side, according to the nearby Marjayoun Hospital.

Rear Adm. Daniel Hagari, an Israeli military official, told reporters the situation at the northern border was calm after the exchange. But he said fighting was still underway in the south and that there were still hostage situations there.

He said troops had moved into every community near the Gaza frontier, where they planned to evacuate all civilians and scour the area for militants.

“We will go through every community until we kill every terrorist that is in Israeli territory," he said. In Gaza, “every terrorist located in a house, all the commanders in houses, will be hit by Israeli fire. That will continue escalating in the coming hours.”

Hamas said that overnight it had continued to send forces and equipment into “a number of locations inside our occupied territories,” referring to Israel. Hamas-linked media reported that the son of Nizar Awadallah, a senior political official, was killed. The Islamic militant group has not reported any senior members being captured, killed or wounded.

The surprise attack Saturday was the deadliest on Israel in decades. In an assault of startling breadth, Hamas gunmen used explosives to break through the border fence enclosing Gaza, then crossed with motorcycles, pickup trucks, paragliders and speed boats on the coast.

They rolled into as many as 22 locations outside the Gaza Strip early Saturday morning, including towns and other communities as far as 24 kilometers (15 miles) from the Gaza border, while Hamas launched thousands of rockets at Israeli cities.