Prime Minister Benjamin Netanyahu of Israel said operations were underway to clear the militants from infiltrated towns and that he had issued a call-up of reservists. “We are at war,” he said in a televised statement.

At least one woman was killed in the initial barrages, according to Israel’s ambulance service, Three Israeli hospitals together reported more than 100 wounded. Soroka Medical Center in the southern city of Beersheba had admitted more than 80 people, with some “in very difficult condition,” a hospital spokeswoman said.

The Israeli military declared “a state of alert for war” and said that its fighter jets had begun airstrikes on the Gaza Strip.

Muhammad Deif, the leader of the military wing of Hamas, the Islamic militant organization that controls Gaza, said in a recorded message that the group had decided to launch an “operation” so that “the enemy will understand that the time of their rampaging without accountability has ended.”

The assault began without any warning about 6:30 a.m. on the Jewish Sabbath and the morning of a festival, the last of the series of Jewish high holidays. It was almost 50 years to the day after the surprise attack by Egyptian and Syrian forces over Israel’s northern and southern borders at the opening of the 1973 war that traumatized the nation.

Within the first hour of the attack, salvos of rockets had slammed relentlessly into Israeli towns and cities, striking as far north as Rishon LeZion, about 10 miles south of Tel Aviv, and Ramla, near Israel’s international airport. At 8:15 a.m. sirens also sounded in central Jerusalem, and loud booms could be heard.

Unverified images on television showed armed gunmen in a pickup truck shooting inside an Israeli community as well as at least one hang-glider in the sky. The militants who crossed the border into Israeli territory were heavily armed, according to Israeli media reports.

Here is the latest:

• Fighting was occurring in two Israeli towns, as well as at the Erez border crossing, according to the Israeli military spokesman, Lt. Col. Richard Hecht.

• Al Qassam Brigades, the military wing of Hamas, said that a military operation “in defense of the Aqsa mosque,” the hotly contested holy site in Jerusalem that thousands of Jews have visited in recent weeks, and against the Israeli blockade.

• The ambulance service, Magen David Adom, issued an urgent call for blood and was organizing a special blood donation drive at a hospital in central Tel Aviv.