He said Egypt would continue efforts to broker a long-term ceasefire.
The spokesperson tried to highlight the Israeli narrative that victims on the Palestinian side are in retaliation for their own rocket attacks, which reportedly affected southern Israel.
Israeli and Hamas officials both threatened a further intensification of hostilities.
"The U.N. says Gaza will be unlivable by 2020", IMEU observes.
In a tweet, the Israeli military said Hamas, the Palestinian militant group that controls Gaza, had "used the building for military purposes".
A picture taken on August 8, 2018 shows a fireball exploding during Israeli air strikes in Gaza City. Despite the animosity, the enemies have signaled, through their contacts with Egypt, that they want to avoid another war.
The military also said that the train service between Ashkelon and the Gaza border town of Sderot would resume.
But the continued outbursts of fire have jeopardized those cease-fire efforts. The military said more than 180 rockets and mortar bombs were fired from Gaza.
In that incident, two fighters from Hamas's military wing were killed by Israeli fire along the border.
The incident occurred while a group of senior Hamas leaders from overseas were visiting Gaza to discuss the ceases-fire efforts with local leaders.
"You can see that when the rockets are raining down, our young people march toward martyrdom", Nofal said.
In New York, Israeli Ambassador to the United Nations Danny Danon called on that body's secretary-general and Security Council members to condemn Hamas's rocket fire against Israel. One Israeli soldier was killed by a Gaza sniper during this period. The ministry said Khammash was also pregnant.
The mother and daughter died immediately and the father is in critical condition, Kamal said.
Israel's military said the five-storey building was used by Hamas's "interior security forces for military purposes".
The Israeli military said it struck some 200 targets throughout Gaza, including Hamas command posts and weapons production and storage facilities. The military said that the Iron Dome aerial defense system intercepted at least 30 rockets and the majority landed in open areas.
"I do not think that any of the other players have any appetite to raise the tensions on their front".
Lt. Col. Jonathan Conricus, a military spokesman, said Israel had "ground troops that are ready to deploy". Israeli Defense Minister Avigdor Lieberman warned last month that Israel is preparing to launch a "large and painful military operation", and Thursday's bombardment appeared to be a step in that direction.
In a statement Thursday morning, the UN Special Coordinator for the Middle East Peace Process Nickolay Mladenov said he was "deeply alarmed" by the flare-up.
He added that "if the current escalation however is not contained immediately, the situation can rapidly deteriorate with devastating consequences for all people".
Palestinians gather around a building after it was bombed by an Israeli aircraft, in Gaza City, Aug. 9, 2018.
The Hamas official, speaking on condition of anonymity because he was discussing classified negotiations, said that cease-fire talks were in their final stage but that disagreements remained.
A more than decade-long Israeli air, land, and sea blockade has crippled Gaza's economy, which boasts one of the highest unemployment rates in the world at 44 percent, leaving an estimated 80 percent of the territory's population dependent on humanitarian assistance.
Israel's prime minister convened his Security Cabinet late Thursday to plot a response to a new burst of violence with Gaza militants, ordering the army to take unspecified "strong action" as the military reinforced units along the border ahead of a possible escalation. The protests have been aimed in part at trying to break the blockade.
A Hamas militant was also killed in the strikes and at least 12 others injured, the Health Ministry said. This comes less than 24 hours after Israeli airstrikes killed three Palestinians on Wednesday night.
A magnitude 7.0 quake struck at a depth of 33km about 154km south-southwest of Puerto Triunfo in El Salvador.
The army's rhetoric has been echoed by Israeli politicians and government bodies over the course of Thursday, with the Foreign Ministry saying that Israel was "defending itself from from Hamas' aggression".