In what appeared to be a step to bolster the Egyptian efforts, organizers announced the cancellation of the weekly protests along the Gaza-Israel frontier, an activity that has been going on for a year and has often led to a violence flare-up.
Palestinian news media reported strikes throughout Gaza, from Rafah in the south to the north of the densely populated coastal strip that is home to two million Palestinians.
Explosions could be heard throughout the night in Gaza and fireballs lit the sky.
Thursday's rocket salvo was the first to be fired toward the greater Tel Aviv area since Israel's devastating 51-day onslaught against Gaza in mid-2014.
The airstrikes followed a rare rocket attack on the Israeli metropolis of Tel Aviv late Thursday.
Tel Aviv Mayor Ron Huldai called to open all the city's bomb shelters as a precaution against any further attacks.
The two rockets had struck late Thursday, taking Israel's military by surprise.
Islamic Jihad said Friday that Palestinian militants would hold fire if Israel did the same.
Naftali Bennett, a right-wing member of Netanyahu's security cabinet whose party is competing against the veteran prime minister's for votes in the coming election, demanded that Israel resume its assassination of Hamas chiefs.
Israel said its aircraft hit around 100 Hamas targets, including an office complex allegedly used by Hamas to coordinate militant operations in the occupied West Bank.
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.
It also targeted the headquarters in the Rimal neighborhood of central Gaza, which is where Hamas directs its organization in Judea and Samaria, the Jerusalem Post reported. Four people were wounded, health ministry officials said.
The apparent misfire came as Gaza's Hamas rulers were in negotiations with Egyptian mediators about a truce deal with Israel.
In a statement, it said its rocket sirens were activated in communities near the Gaza Strip border on Friday soon after it carried out strikes on Hamas targets in the territory. "No interceptions were made by aerial defense systems". 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.
It comes with the one-year anniversary of mass protests and clashes along the Gaza-Israel border fence approaching on March 30.
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