Among targets hit were a military compound used to produce rockets and the organizations command center.
The announcement also said Israel views the ceasefire violations and rocket launches towards Israeli communities, seriously, is maintaining a high alert and will respond against any attempts to cause harm to Israeli civilians.
The fragile ceasefire has been violated by Gaza militants several times since it came into effect. At 5:23pm, sirens were heard in the regional councils Sdeot Negev, Eshkol and Shaar HaNegev. Iron Dome intercepted one rocket, and there were no injuries or damage reported.
Between 6am and 7am, several more rockets were fired from the Gaza Strip into the Gaza-area communities, also without causing casualties or damage.
At 10:54 am, five rockets were launched from the Gaza Strip at Israeli communities bordering the Strip. Iron Dome intercepted two of them.
In this case, too, there were no injuries or damage.
Sirens sounded again in the late afternoon.
Rocket alert sirens blared over Sderot near the Gaza border in the late hours of the evening as the Iron Dome missile defense system intercepted two projectiles in the sky over the city.
Schools will remain closed Friday in many southern communities.
"Following the rocket sirens in the area, the forum of the heads of the Gaza border councils decided that tomorrow (Friday) there will be no studies at any educational institutions in the councils surrounding Gaza," the heads of the local authorities said in a joint statement.
"We are in contact with the IDF and are monitoring developments," the statement said, adding that, "The decision was made out of concern for students and educational staff."
The decision was met however with outrage from some local residents.
"It's the wrong decision that impacts adversely on our resilience, it's a surrender to terrorism," they said.
In northern Gaza, protesters took to the streets following a spontaneous social media drive to call for continued rocket strikes on Israeli population centers.
Abu Hamza, the spokesman for the Islamic Jihad military wing, said Thursday evening: "Our fighters in all military units still have their fingers on the trigger and are functioning in an integrated military system. They are at the disposal of the organization's leadership."
Gaza medical officials have put the death toll from the two days of fighting at 34 Palestinians, almost half of them civilians and including eight children and three women.
Hundreds of rocket launches by militants had paralysed much of southern Israel and reached as far north as Tel Aviv, sending entire communities to shelters. Dozens of Israelis were hurt.
Hamas, Gaza's dominant faction, appeared to have stayed out of this round of fighting. That may have helped stem escalation.
The violence began early Tuesday, with a predawn Israeli strike in Gaza that killed Islamic Jihad commander Baha Abu al-Ata. The organization vowed revenge and while Hamas expressed its solidarity, by Wednesday night it had yet to engage in the fighting.
The rocket attacks on Israel followed soon after Abu al-Ata's killing, and on Tuesday the south and large parts of the center of the country came close to a standstill as schools were closed and all non-essential workers were told to stay home or near a bomb shelter.
Rockets were intercepted by Iron Dome as far north as Tel Aviv, with attacks also targeting nearby cities of Holon and Rishon Lezion.
The army said Thursday that the missile defense system had had a 93% success rate.