The sudden outburst of fighting comes at a sensitive time for both sides.
Israeli Prime Minister Benjamin Netanyahu is in the midst of a tight re-election battle.
Brig. Gen. Ronen Manelis, the chief Israeli military spokesman, said the army had been caught off guard by Thursday night's rocket barrage.
The IDF estimates that the two rockets launched by Hamas into metropolitan Tel Aviv was made in error, and Hamas did not intend to carry out an attack. Though the attack caused no damage or injuries, it was a significant escalation and set the stage for a tough Israeli reprisal.
Tel Aviv Mayor Ron Huldai said he had ordered the city to open public air raid shelters as a protective measure.
The Hamas-controlled Gaza Interior Ministry labeled Thursday's rocket attacks targeting Tel Aviv "outside of the national consensus", with Hamas claiming it would clamp down on those responsible.
Israel's response reportedly went into Friday morning as Hamas continued firing several rounds of rocket fire.
The terror sites included "an office complex in Gaza City used to plan and command Hamas militant activities, an underground complex that served as Hamas' main rocket-manufacturing site and a center used for Hamas drone development", according to an Associated Press report.
Israeli officials say that amounts to calling for the Jewish state's destruction, and accuse Hamas, the Islamist movement that runs the Gaza Strip, of orchestrating the protests.
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Netanyahu has organized the attack on the innocent people of the Gaza Strip to achieve this sinister goal, he noted.
Three were intercepted by missile defence systems, it said.
Nearly daily exchanges between Israel and the Palestinian territory have threatened a wider escalation in hostilities over the past few weeks.
They added that protests will resume in the coming weeks, with particular preparation for the one-year anniversary of their beginning on March 30, AFP reports. The assessment indicated that Hamas had no intention of escalating violence with Israel. Israel and Egypt have maintained a crippling blockade on Gaza since Hamas took over the territory in 2007.
"I've heard people in Gaza saying that since we're in an election campaign, a large-scale operation is out of the question", he said.
Danon slammed Hamas saying it uses civilians "as human shields" and that "a terrorist organization that tries to harm Israel will encounter a relentless and uncompromising force".
No militant groups have said they fired the rockets at Tel Aviv.
"Two rockets were launched from the Gaza Strip towards Israeli territory".
It was the first time there has been such an attack since the war in 2014.
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