Israeli Prime Minister Benjamin Netanyahu is in the midst of a tight re-election battle.
The late-night attack Thursday on Tel Aviv, Israel's densely populated commercial and cultural capital, marked the first time the city had been hit since the 2014 war.
Sirens were set off, but there were no immediate reports of damage or casualties.
Israel's Channel 10 news, citing anonymous military officials, said the rockets were Iranian-made Fajr rockets.
One rocket probably fell into the sea, Tel Aviv's mayor, Ron Huldai, told Israeli television.
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Both Hamas, the Islamist movement that runs Gaza, and its ally Islamic Jihad denied they were behind the rocket fire toward Tel Aviv, raising the possibility they were launched by fringe groups.
The military said two rockets were launched from the Gaza Strip and it would provide further details later.
But Israel's military concluded that Hamas was responsible.
"The protest was started by just dozens of people in Jabalia and picked up the pace in the city of Deir al-Balah, but towards the late evening hours, the demonstrators began to disperse", said a Palestinian source in Gaza.
Among the terrorist targets was the offices of the Hamas headquarters in Gaza City responsible for directing terrorist operatives in Judea and Samaria, building terrorist infrastructures and transferring money to those responsible for terrorist attacks against Israeli citizens.
"We don't know who carried it out", Manelis said, adding: "The Hamas organisation is the main organisation in the Strip".
The warplanes targeted Palestinian positions in the north and south of the coastal enclave.
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Despite its denial, Hamas is one of the only groups in Gaza with the means to strike Tel Aviv.
Andrew Carey reported from Jerusalem and Ibrahim Dahman from Gaza.
Sirens rang out in southern Israel early Friday and the Israeli military said it identified four "launches" from Gaza. The organizers of a weekly protest along the Israeli border said they would cancel the demonstration in the wake of the escalation.
Nearly daily exchanges between Israel and the Palestinian territory have threatened a wider escalation in hostilities over the past few weeks.
The Hamas administration vowed to "take measures" against those behind the salvo, which it described as violating the "factional and national consensus" governing Gaza.
Naftali Bennett, a member of Netanyahu's security Cabinet who is vying against him for rightist votes in the looming election, demanded the assassination of Hamas chiefs.
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