Mohammad Deif, 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 end the last occupation on earth," he said, adding that 5,000 rockets had been launched.

One Israeli woman was killed, according to emergency services, as ambulance crews were deployed in areas around the Gaza Strip and sirens sounded across Israel, including Jerusalem.

Israeli media reported that gunmen had opened fire on passersby in the town of Sderot, in southern Israel, and footage circulating on social media appeared to show clashes in city streets.

"A number of terrorists have infiltrated into Israeli territory from the Gaza Strip," the military said in a statement, adding that residents in the area surrounding the Gaza Strip had been told to stay in their homes.

"The Israeli Defence Forces will defend Israeli civilians and the Hamas terrorist organization will pay heavy price for its actions," it said.

Prime Minister Benjamin Netanyahu's office said he would meet top security officials in the coming hours.

In Gaza the roar of launches could be heard and residents reported armed clashes along the separation fence with Israel, near the southern town of Khan Younis and said they had seen significant movement of armed fighters.

Israel's ambulance service said teams had been dispatched to areas in southern Israel near Gaza and residents were warned to stay inside.