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Several people have been injured at the Holy Family Church in Gaza City, with some unconfirmed reports that it was hit by Israeli artillery shells.
Catholic Church leaders referred only to it being "struck by a raid" in a statement, but Italy's prime minister blamed Israeli forces.
The Israeli military said it was aware of the reports of damage and casualties at the church, adding that "the circumstances of the incident are under review".
Many displaced Christian families from the small local community have been living in the Roman Catholic church since the war began after their own homes were destroyed. While he was alive, the late Pope Francis called them on a near-daily basis.
The Latin Patriarchate in Jerusalem said the Argentine parish priest, Father Gabriel Romanelli, was among those injured and denied initial reports of fatalities.
It added that the church had been damaged.
A video and photos shared with the BBC showed the roof was hit, close to the cross, and that windows were broken.
The Latin Patriarchate said it would provide additional details when they were confirmed.
A video aired on Arab TV showed Father Gabriel walking unsteadily and checking on a man on a stretcher at the Al-Ahli Hospital in Gaza City, where those injured are being treated.
Italian Prime Minister Giorgia Meloni blamed Israel, saying: "The attacks against the civilian population that Israel has been carrying out for months are unacceptable."
"No military action can justify such an attitude," she added.
The Vatican has so far not responded to a request for comment.
The Greek Orthodox Patriarchate in Jerusalem condemned the strike, which it called a "flagrant violation of human dignity and a blatant violation of the sanctity of life and the sanctity of religious sites, which are supposed to provide a safe haven in times of war".
It estimated that 600 displaced people were sheltering inside at the time, the majority of whom were children as well as 54 people with special needs.
The Holy Family Church falls within part of Gaza City that the Israeli military has previously told locals to leave.
Israel launched its war in Gaza in retaliation for the Hamas-led attacks on 7 October 2023, which killed about 1,200 people and led to 251 others being taken hostage.
Israeli attacks have since killed more than 58,500 people in Gaza, according to the Hamas-run health ministry. The ministry's figures are quoted by the UN and others as the most reliable source of statistics available on casualties.