Dozens of armed men from the Palestinian militant group Hamas have infiltrated southern Israel in a surprise attack from the Gaza Strip.
Videos emerged on social media showing Palestinian militants shooting at passers-by on the streets of the Israeli town of Sderot.
Intense Palestinian rocket fire from Gaza also killed one Israeli woman.
Israel’s defense minister said Hamas “made a serious mistake and started a war” against his country.
“[Israeli] forces are fighting the enemy in every location,” Yoav Gallant added. “The State of Israel will win this war.”
The Israeli Defense Forces (IDF) said it was in a war situation and dozens of fighter jets carried out airstrikes on Hamas locations in Gaza.
The rocket fire from Gaza – which is ruled by Hamas – began just after dawn on Saturday, at the end of the Jewish holiday of Sukkot.
As sirens sounded across Israel, the IDF announced that “terrorists” had infiltrated Israeli territory “in a number of different locations.”
It told civilians in the southern and central areas to stay next to shelters, and in shelters in the Gaza area.
Images posted online appeared to show a group of heavily armed Palestinian militants dressed in black fatigues driving through Sderot in a pickup truck.
In one video, the same militants appeared to exchange fire with Israeli forces on the streets of the city, which is just 1 mile (1.6 km) from Gaza.
There are also unconfirmed reports in the Palestinian media that a number of Israelis have been captured by militants and images of Palestinians in Gaza driving Israeli military vehicles are circulating.
The rocket fire, meanwhile, continued throughout Saturday morning, with Israeli media reporting that more than 2,200 projectiles had been fired into Israel so far.
An initial report from Israeli ambulance service Magen David Adom said one person had been killed in the rocket attacks and 16 others had been injured, two of them seriously.
But a hospital in the southern city of Ashkelon later said it was treating 68 victims alone, while another hospital in Beer Sheva reported 80 others.
A senior Hamas military commander announced the start of the operation in a broadcast on Hamas media, calling on Palestinians around the world to fight.
“This is the day of the greatest struggle to end the last occupation on earth,” said Mohammed Deif.