"The IDF holds the Hamas terror organization responsible for all events transpiring in the Gaza Strip and emanating from it", the military said in a statement.
In Gaza, both rulers Hamas and Islamic Jihad, an allied group, issued statements denying any responsibility for the attack, which came just over three weeks ahead of Israel's April 9 election. Witnesses said the powerful explosions from the air strikes rocked buildings in Gaza and lit up the skies over the targeted sites.
But Hamas denied responsibility and Israeli media, including Ha'aretz and Channel 7 News, later carried reports that the rockets might have been fired from Gaza by mistake.
Israeli media received information from defense officials saying a preliminary investigation determined that the Hamas rockets were misfires.
The apparent rocket fire came in response to Israeli airstrikes, launched after an early rocket attack on Tel Aviv.
That salvo caused no casualties or damage, missing built-up areas.
Netanyahu called an emergency meeting with top security officials, after which Israel mounted its response.
World Jewish Congress CEO and Executive Vice President Robert Singer voiced extreme concern on Thursday after two missiles were fired by Palestinian militants in the Gaza Strip. Israel and Egypt have maintained a crippling blockade on Gaza since Hamas took over the territory in 2007.
The fighting broke out as Egyptian mediators were in Gaza trying to broker an expanded cease-fire deal between the bitter enemies.
"In keeping with the public interest, the commission has made a decision to exceptionally postpone its activities scheduled for this day", the body which organizes the protests said in a statement.
But it marked the first time that Tel Aviv, some 50 miles north of Gaza, has been targeted by rocket fire since a 2014 war with Gaza militants.
Also Friday, a Hamas official said an agreement to restore calm has been reached.
The organisers of Palestinian demonstrations that usually take place along the Gaza border have canceled Friday's protest, hours after an exchange of fire between Gaza and Israel flared up tensions in the region. The assessment indicated that Hamas had no intention of escalating violence with Israel.
"I suggest to Hamas, don't count on it", he told his Cabinet. Hamas possesses a large arsenal of rockets and missiles capable of striking deep inside Israel.