Air raid sirens wailed across southern and central Israel, with the army urging people to stay close to bomb shelters.
The armed wing of the Palestinian group Hamas announced it was behind the aerial assault, claiming its fighters had launched more than 5,000 rockets.
Israel’s military said Hamas launched “massive shooting of rockets”, while at the same time “terrorists infiltrated into Israeli territory in a number of different locations”.
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.
Israel has imposed a crippling blockade on Gaza since 2007 after Hamas took power.
Palestinian fighters and Israel have fought several devastating wars since.
The latest violence follows a period of heightened tensions in September, when Israel closed the border to Gaza workers for two weeks.
So far this year at least 247 Palestinians, 32 Israelis and two foreigners have been killed in the conflict, including fighters and civilians on both sides, according to Israeli and Palestinian officials.
The vast majority of fatalities have occurred in the West Bank, which has been illegally occupied by Israel since the 1967 Arab-Israeli conflict.