Medical officials said at least seven people were wounded in airstrikes on the five-storey building, a popular theatre venue in the Shati refugee camp in the Palestinian territory.
The Israel Defense Forces (IDF), posting video of the strike on Twitter, said the building had been used for military purposes. Hamas claimed its own offices near the site of the cultural centre had not been struck.
Hamas spokesman Hazem Qassem said: “The deliberate targeting of a cultural centre with airstrikes and destruction... is a barbaric act.”
It appeared to be the last in a series of Israeli strikes on the Palestinian enclave since fighting with Hamas began on Wednesday.
The Hamas TV channel Al Aqsa reported late Thursday that a ceasefire brokered by Egypt had taken hold “on the basis of mutual calm”.
A senior Hamas official, speaking on condition of anonymity, told the Associated Press the agreement merely ended the latest round of violence, and no long-term ceasefire deal had been reached.
Israeli authorities have yet to confirm any agreement was made, but reports of calm from Gaza on Friday morning appeared to suggest a ceasefire was in place and holding.
The deal is set to be tested later today, however, when Palestinians in Gaza plan on resuming their weekly border protests.
Shortly before the attack on the cultural centre, a Palestinian rocket struck the southern Israeli city of Beersheba late on Thursday afternoon, landing in an open area. It was the first time a rocket had reached the city since the 2014 conflict between the two sides.
The Palestinian Health Ministry said three Palestinians, including a pregnant woman and her one-year-old daughter, were killed in Israeli airstrikes on Wednesday night.
Israeli officials said seven people had been wounded by rocket or mortar fired into Israel by Hamas militants.
The IDF blamed the latest outbreak of fighting on Hamas, claiming militants opened fire on an IDF vehicle in Gaza on Wednesday.
A Hamas spokesperson, however, claimed Israeli forces had killed two Hamas fighters carrying out a military exercise in northern Gaza in an “unprovoked” attack.
On Thursday Gaza’s Health Ministry identified those killed in subsequent airstrikes as 23-year-old Enas Khamash and her daughter Bayan, and a Hamas fighter named Ali Ghandour.
Tension along the Israel-Gaza border has escalated since March, when Hamas launched mass protests along Israel’s perimeter fence with Gaza.
It was aimed at trying to break the Israeli-Egyptian border blockade: Gaza’s economy has been hit hard by the total blockade imposed back in 2007.
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