Gaza militants often vacate potential target sites during flare-ups and Israelis who live in villages and towns near the border have reinforced rooms in their homes and rocket sirens that alert of an incoming attack.
Thousands took part in Friday's protests, which marked 100 days since their launch, with some venturing close to the border fence, burning tires and throwing stones. Over 11,100 others - including 3,374 children, 2,088 women and 410 elderly people - were also wounded in the war. There were no immediate reports of any casualties.
The IDF also destroyed two border-crossing attack tunnels, Hamas naval facilities and dozens of other military compounds.
Even as the airstrikes were being carried out, the IDF said rockets were fired toward Israel. Some were intercepted by Israel's Iron Dome missiles. One rocket landed inside a kibbutz in the Shar HaNegev Regional Council area.
Hamas spokesman Fawzi Barhoum said the Palestinian resistance movement had agreed to an "Egyptian offer to return to a ceasefire to stop this escalation".
With Israel focused on efforts to prevent Iran from establishing a permanent military foothold in neighboring Syria, it has been wary of escalating violence in Gaza. Striking in the heart of Gaza City is typically only seen during full-blown conflicts like the 2014 war and could signal that a further escalation may be in store.
In fresh violence Friday, a 15-year-old was shot dead during the demonstrations and a 20-year-old died later of gunshot wounds sustained during the protest, the Gaza health ministry said.
Israeli military spokesman Lieutenant Jonathan Conricus said the objective of Saturday's operation was to stop arson attacks, attempted border breaches, and assaults on soldiers from Gaza that have grown increasingly violent.
"We were sitting in the living room and all of a sudden, the aquarium exploded and there was smoke everywhere and glass flew everywhere", said Aharon Buchris, who was wounded along with his wife and two teenage daughters, as he awaited surgery in hospital.
Israel has been the target of some 200 rockets and mortars over the past 24 hours targeting southern communities near the Gaza border.
Earlier in the day, during the weekly Great March of Return protest, an IDF officer was moderately injured by a grenade thrown from the Gaza Strip.
During the day's fighting, Gaza militants fired more than 90 mortar bombs and rockets toward Israel, the military said, setting off sirens and sending Israelis fleeing to shelters. Humanitarian and essential supplies continue to enter Gaza. The IDF retaliated against the most recent attack.
On Wednesday, incendiary kites and balloons sparked 19 fires of varying sizes in Israel, according to local government officials. The other four occurred in the Sha'ar Hanegev region, which lies to the northeast of the coastal enclave.