But the continued outbursts of fire have jeopardized those cease-fire efforts.
According to Haaretz, the Israeli Defense Forces (IDF) intentionally targeted civilians "with the goal of causing the residents to understand the price of escalation and placing Hamas in a problematic situation".
Residents said the building had served mainly as a cultural centre.
A Hamas militant was also killed in the overnight strikes and at least 12 others injured, the health ministry said.
After a four-hour meeting of Israel's security cabinet on Thursday the Ministerial Committee on National Security Affairs said in a statement that "the cabinet instructed the IDF to continue to act with force against terrorist elements".
Hamas is demanding the lifting of an Israeli-Egyptian border blockade that has devastated Gaza's economy, while Israel wants an end to rocket fire, as well as recent border protests and launches of incendiary balloons, and the return of the remains of two dead soldiers and two Israelis believed to be alive and held by Hamas.
The military said more than 180 rockets and mortar bombs were fired from Gaza.
Strikingly, the word "respond", or any variation thereof, appears only in context of Hamas responding to Israeli strikes: "Hamas, the Islamic militant group that has ruled Gaza for 11 years, has been trying to change the balance of deterrence in the area, responding to every Israeli strike against Gaza".
Most of the rockets fired by Palestinian militants landed in open areas, but at least two hit the Israeli town of Sderot and sirens sounded throughout the night.
Mohammed Salem ReutersPalestinians gather around a building after it was bombed by an Israeli aircraft in Gaza City Aug. 9 2018
Conricus wouldn't comment on Israeli media reports of troops preparing for a possible ground operation, but said Israel "had ground troops that are ready to deploy".
Mladenov warned that "if the current escalation however is not contained immediately, the situation can rapidly deteriorate with devastating consequences for all people".
Earlier in the day, Hamas deputy chief in Gaza Khalil al-Hayya said efforts to reach a truce with the Israeli regime were at "an advanced stage".
"Factions of the resistance consider this round of escalation over as far as we are concerned, and the continuation of calm depends on the behaviour of the occupation", the Palestinian official said, using militant groups' term for Israel.
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.
Israel's latest bombing campaign in Gaza comes just weeks after Israeli F-16s carried out "wide-scale" airstrikes throughout the occupied territory.
Since March 30, more than 150 Palestinians have been killed, according to the Palestinian Health Ministry.
Palestinian President Mahmoud Abbas earlier urged the United Nations to stop Israel's latest aggression against Gaza, which has been under a crippling Israeli siege for the past decade.
A magnitude 7.0 quake struck at a depth of 33km about 154km south-southwest of Puerto Triunfo in El Salvador.
"As we approach a potential agreement, it's extremely important for Hamas to deliver the message that we are not going there because we are weak", said Yossi Kuperwasser, a retired brigadier general and the former director general of Israel's Ministry of Strategic Affairs. But it has come under heavy worldwide criticism for its frequent use of force against unarmed protesters.
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