About 270 rockets were fired from Gaza into Israel early Wednesday afternoon.
The roadblock was in response to Israeli strikes on Monday, which killed three senior Islamic Jihad commanders and 10 civilians and injured 20.
Air raid sirens sounded in the border towns of Sderot, Ashkelon and Ashdod and further up the coast in Tel Aviv.
Witnesses said they saw the Iron Dome missile defense system intercepting rockets near the city.
Israeli media said there was a direct hit on a kindergarten near the Gaza Strip, but no injuries were reported. Schools have been closed since Tuesday.
Flights were briefly prevented from landing at Ben Gurion Airport, but operations have now resumed. A British Airways flight has been diverted to Larnaca in Cyprus.
An Israel Defense Forces spokesman insisted that Palestinian Islamic Jihad was behind the rocket fire, not Hamas, the group that controls the Gaza Strip. However, Hamas publicly supported the rocket attacks.
Israel launched “Operation Shield and Arrow” in the early hours of Monday morning after rockets were fired at it last week.
Military officers said they killed the men responsible for the attacks and said they planned assaults on Israel.
Children among the dead as Israel kills three Islamic Jihad commanders
Two women killed in West Bank shooting
The IDF confirmed that the commanders killed were Khalil Bahitini, who led PIJ operations in northern Gaza, Tarek Azaldin who allegedly coordinated attacks in the West Bank from Gaza, and Jahed Ahman, a senior member of the group’s military council.
Later on Tuesday, and again on Wednesday, the Israeli Air Force hit targets in Gaza they said were preparing to launch missiles, killing three more people.
Residents near the Gaza border in southern Israel were ordered to stay close to bomb shelters and hundreds were evacuated to towns in the north. Outdoor gatherings were banned and the Erez crossing between Gaza and Israel closed.
Reservists were put on standby and Israel’s Home Command said it remained ready for further action.