It was the largest daytime attack by Israel on the coastal enclave controlled by the Hamas Islamist group since the 2014 Israel-Gaza war, an army spokesman said.
In the other direction "more than 60 rockets" were fired at southern Israel from Gaza, the Israeli military said, of which "approximately 10 rockets were intercepted". There were no reports of injuries and the IDF did not immediately comment.
Earlier on Saturday, Israel said it had launched air strikes targeting Hamas facilities in Gaza, a day after Israeli forces shot and killed two Palestinians demonstrating near the fence separating the enclave from Israel.
Israel's political leadership is considering a range of possibilities for trying to halt the rocket fire, including targeted assassinations of Hamas terror chiefs, the use of ground forces, and a ceasefire mediated by Egypt and/or others, but no decision had been made as of Saturday late afternoon, Hadashot TV news reported.
It marks the first injuries on the Israeli side in the latest flare-up in violence between Israel and Hamas militants. "They were crowned by the success of the Egyptian effort to restore calm and end the escalation".
"We are talking about the biggest offensive strikes since Protective Edge", Brigadier General Tzvika Haimovic told journalists, referring to Israel's name for its 2014 operation in the Gaza Strip.More news: Donald Trump visibly annoyed by question over incendiary Brexit comments
Palestinian health officials said two people were killed and 12 injured in an air strike in Gaza City. A third projectile hit a home in Sderot, wounding three Israelis.
One rocket hit a home in the town of Sderot.
"Troops responded by firing towards the terrorists", the military said.
Sporadic Palestinian rocket attacks and incendiary kites from Gaza that have burned large tracts of farmland in Israeli border areas have increased public pressure on Netanyahu for a stronger armed response.
They will abide by the cease-fire as long as Israel does, Shiha said.
"The action we are taking draws a clear red line: that from now on, we will not allow this".More news: Best states for retirement
Israel says it has struck dozens of Hamas military targets in northern Gaza in retaliation for assaults including more than 90 rocket attacks. A 15-year-old Palestinian was shot dead as he tried to climb over the fence into Israel. Fourteen others were wounded. Nearby houses were damaged. "We have no intention to harm anyone who is not a terrorist", he said.
The exchange of fire followed months of tension that has raised the prospect of a fourth war in the blockaded Gaza Strip since 2008. A police spokesman said no hits had been identified in the city.
Among the main targets was the "Hamas Battalion HQ in Beit Lahia, which includes urban warfare training facilities, (a) weapon storage warehouse, training compounds, command centres, offices and more", the Israeli army said in a statement. "Bombardment for bombardment", he said.
In advance of Friday's protest, the organising committee called on Palestinians to take part in the protests to express solidarity with Khan al-Ahmar, a Bedouin village in the occupied West Bank slated for total demolition by Israeli authorities. However, the Israeli army said one soldier was wounded by a grenade on Friday.
Hours later, the military launched a series of airstrikes in Gaza.
Organisers say the demonstrations aim to press demands for a right to lands lost to Israel in the 1948 war of its foundation and for the blockade to ease.More news: Djokovic 'overwhelmed' after downing Nadal in Wimbledon classic
The conflicts have killed thousands of Palestinians, mostly civilians.