Former Defense Minister and head of Yisrael Beitenu, Avigdor Liberman, called on Israel to "return to the policy of punishing those responsible".
Organisers of weekly Friday protests along the Gaza border fence, which have been accompanied by violence, announced they would be cancelled - the first such move since they began almost a year ago.
The Israeli military said "it appears" that two rockets were launched from Gaza. Israel holds Gaza's Hamas rulers responsible for all fire out of the territory. The strikes were a response to terrorist rocket attacks that targeted southern Israel and as far away as Tel Aviv.
A military spokesman declined to comment.
Israel and Hamas are bitter enemies and have fought three wars since the Islamic militant group seized power in Gaza in 2007.
Israel strikes Gaza after two rockets fired at Tel Aviv
Reuters was unable to immediately verify the claims.
The 2014 Gaza War was the third between Israel and Hamas in a decade. In addition it hit an underground complex that served as Hamas' main rocket-manufacturing site, and a military training site that also functioned as the group's drone program.
Witnesses said the powerful explosions from the air strikes rocked buildings in Gaza and lit up the skies over the targeted sites.
The anniversary of the Gaza border protests is in two weeks, on March 30 and Palestinian groups have been preparing events and march to mark the date. "People are afraid of bombs -- like in a war".
"The terrorists that fired these rockets into Israel's most populated civilian area did so while hiding behind Palestinians civilians in Gaza and exploiting them as human shields". Shortly afterwards, the Israeli air force launched a series of strikes targeting Hamas naval bases in Gaza.
On Friday, Islamic Jihad's armed wing said in a statement that it had put its fighters on full alert to respond to Israeli attacks. Rocket fire persisted throughout the morning, setting the stage for possible additional reprisals.
Nearly daily exchanges between Israel and the Palestinian territory have threatened a wider escalation in hostilities over the past few weeks. The assessment indicated that Hamas had no intention of escalating violence with Israel. It's a first since Israel's 2014 campaign in 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.