Hamas, which dominates Gaza, insisted it was not behind the rocket fire.
Netanyahu's main rivalry in the upcoming elections, former army chief of staff Benny Gantz and leader of the Blue and White party said, "Only an aggressive and severe response" was necessary, "otherwise it will be impossible to renew our deterrence".
It is the beginning of one of the worst escalations in years, with hundreds of rockets and mortars fired at Israel and dozens of Israeli strikes against Gaza positions.
This is a breaking news story and is constantly being updated.
The warplanes could be heard flying overhead in Gaza City, where smoke from the explosions could be seen in the distance.
However, following the start of Israel's airstrikes against Gaza, the IDF confirmed via Twitter that the rockets were those of Hamas.
The sudden outbreak of violence came at a sensitive time for both sides.
There were no reports of casualties in Gaza.
Israeli defense officials said after a preliminary investigation that the Gaza rockets that hit the Tel Aviv area were apparently fired by mistake. Israel holds Gaza's Hamas rulers responsible for all fire out of the territory.
Two long-range rockets fired from Gaza exploded in Tel-Aviv during rush hour Thursday evening.
Israel and Hamas have fought three wars since the Islamic militant group seized power in Gaza in 2007.
Calm was restored by mid-morning as an Egyptian delegation mediated between Israel and Palestinian factions, a Palestinian official said.
The March of Return protests have taken place weekly along the border since last March and have periodically escalated into major flareups between the Israeli military and Gaza-based terror groups.
In an unusual step that indicated Hamas was attempting to prevent further escalation, the Hamas Interior Ministry said the rocket fire went "against the national consensus" and promised to take action against the perpetuators.
It was the first time the city had been targeted since a 2014 war between Israel and Gaza militants.
Despite its denial, Hamas is one of the only groups in Gaza with the means to strike Tel Aviv.
"I suggest to Hamas, don't count on it", he told his Cabinet. A smaller militant group that also possesses a large arsenal of rockets, the Iranian-backed Islamic Jihad, also denied involvement.