Officials in Tel Aviv say that "Palestinian militants have begun a 'war' against Israel via air, sea and land" from the blockaded Gaza Strip on Saturday, in a major attack which has reportedly killed over 40 Israelis and injured at least 750.
Prime Minister Benjamin Netanyahu said "we are at war" and vowed severe retaliation after ordering an extensive mobilisation of Israeli army reserves. "The enemy will pay an unprecedented price," he warned.
Medical sources in Gaza reported that 160 Palestinians had been killed in Gaza and over 1000 injured in Israeli strikes since the morning.
Israeli attacks in the occupied Palestinian territories have been surging since early last year, with Palestinians killed in the West Bank reaching a death toll as high as 247.
"We decided to put an end to all the crimes of the occupation (Israel). Their time for rampaging without being held accountable is over," said the Ezzedine al-Qassam Brigades, the armed wing of Hamas which controls the Gaza Strip.
"We announce Operation Al-Aqsa Flood and we fired, in the first strike of 20 minutes, more than 5,000 rockets."
Israel's army said its forces were fighting Palestinians on the ground in several locations near the besieged Gaza Strip. It dubbed its operation "Swords of Iron".
Israeli army spokesman Richard Hecht said the militants conducted a combined raid "which happened through paragliders, through the sea and through the ground."
Hamas later released videos showing a number of Israelis captured by its fighters, amid reports that over 35 people had been captured and taken to Gaza by the group.
Infiltration into Israel by fighters from Gaza, an impoverished territory home to 2.3 million people, have been rare since Hamas took control in 2007. Israel imposed a crippling blockade on the territory then and Gaza is sealed off from Israel by a militarised border barrier.
The rocket fire from Gaza - which Hecht said numbered at least 2,200 - left cars burning beneath residential buildings in the Israeli city of Ashkelon, about 10 kilometres (six miles) north of Gaza.
Netanyahu said in a statement Hamas had launched a "murderous surprise attack" against Israel and its people.
The Israeli leader said he had "ordered an extensive mobilisation of reserves" and fire would be returned at "a magnitude that the enemy has not known".
Israeli Major General Ghasan Alyan warned Hamas had "opened the gates of hell" and would "pay for its deeds".
AFP journalists said Israel's military began air strikes on Gaza, following the rocket barrage from inside the territory.
"Dozens of IDF fighter jets are currently striking a number of targets belonging to the Hamas terrorist organisation in the Gaza Strip," the military said.
Rockets had streamed across the sky after the first launches from multiple locations across the Palestinian territory from 6:30 am (0330 GMT), AFP journalists in Gaza City reported.
An AFP journalist saw Palestinians gathered around an Israeli tank, which was partially in flames, after they crossed the border fence from Khan Yunis in Gaza.
Another AFP journalist saw Palestinians returning to Gaza City driving a seized Israeli Humvee.
Air raid sirens could be heard across southern and central Israel, as well as an unusual number of times in Jerusalem, where AFP journalists heard multiple rockets being intercepted by Israeli air defence systems.
The army urged people to stay near bomb shelters.
Israeli police set up roadblocks to check motorists on the highway between Tel Aviv and Jerusalem, an AFP journalist said.
Hundreds of residents fled their homes in Gaza to move away from the border with Israel, mostly in the northeastern part of the territory, an AFP correspondent said, adding the men, women and children carried blankets and food.
In the Israeli commercial centre of Tel Aviv, residents were seen boarding a bus to seek safety in a hotel.
Meanwhile, a regional council for Israeli communities northeast of Gaza said its president was killed due to rocket fire launched from Gaza.
Separately, a woman in her 60s was killed "due to a direct hit" in Israel, the Magen David Adom emergency services said.
Over 750 people are said to be wounded, with 40 in "serious" condition, Israeli media reported.
Hamas called on "the resistance fighters in the West Bank" as well as "our Arab and Islamic nations" to join the battle, in a statement posted on Telegram.
Lebanese militant group Hezbollah, which fought a devastating war against Israel in 2006, hailed the Palestinians' "heroic operation on a grand scale".
Western countries, however, roundly condemned the attacks on Israel.
Gaza and Israel have fought several wars over the years. The latest violence follows heightened tensions in September, when Israel closed the border to Gazan workers for two weeks, with Israelis firing tear gas and live bullets at Palestinians.
Resuming workers' passage on September 28 had raised hopes of calming the situation in Gaza.
In May, an exchange of Israeli air strikes and Gaza rocket fire killed 34 Palestinians and one Israeli.
Most of the violence in the Palestinian territories and Israel has occurred in the West Bank, which has witnessed intensified military incursions and increased settler violence under Prime Minister Benjamin Netanyahu's far-right leadership.
Several ministers under Netanyahu are illegal settlers in the West Bank, and have incited violence and hatred against Palestinians on numerous occasions.