Dozens of gunmen from the Palestinian militant group Hamas have infiltrated southern Israel from the Gaza Strip in a surprise attack.

Videos being shared on social media appeared to show Palestinian militants shooting at passers-by in the streets of the Israeli town of Sderot.

Intense Palestinian rocket fire from Gaza also killed one Israeli woman.

Israel's defence minister said Hamas had "made a grave mistake and launched a war" against his country.

"[Israeli] troops are fighting the enemy at every location," Yoav Gallant added. "The State of Israel will win this war".

The Israel Defense Forces (IDF) said it had moved to a war footing and that dozens of fighter jets were carrying out air strikes on Hamas sites in Gaza.

The rocket barrages from Gaza - which is governed 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 southern and central areas to stay next to shelters, and inside shelters in the area surrounding Gaza.

Footage posted online appeared to show a group of heavily armed Palestinian militants dressed in black fatigues driving around Sderot in a pick-up truck.

In one video, the same militants seemed to be exchanging fire with Israeli forces on the streets of the town, which is only 1.6km (1 mile) from Gaza.

There are also unconfirmed reports in the Palestinian media that a number of Israelis have been taken captive by militants and footage circulating of Palestinians in Gaza driving Israeli military vehicles.

The rocket barrages meanwhile continued throughout Saturday morning, with Israeli media reporting that more than 2,200 projectiles had so far been launched towards Israel.

An initial report from Israel's Magen David Adom ambulance service said one person had been killed in the rocket attacks and 16 others wounded, two of them seriously.

But a hospital in the southern city of Ashkelon later said it was treating 68 casualties 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 everywhere to fight.

"This is the day of the greatest battle to end the last occupation on earth," Mohammed Deif said.