Eight men tasked with protecting aid trucks were reported among the dead in air strikes that were carried out while mediators continued ceasefire talks in Doha.
A US official said this week the talks were going well but two officials from the Palestinian militant group Hamas told Reuters there had been no breakthrough as the Israeli military continued to pummel Gaza.
A man and a woman died, and several people were wounded on Thursday in "an apparent strike by the Israeli army" on Gaza's Holy Family Church, the Latin Patriarchate of Jerusalem said in a statement.
"We pray that their souls rest (in peace) and for an end to this barbaric war. Nothing can justify the targeting of innocent civilians," said the Patriarchate, which oversees the only Catholic church in the enclave.
Photos released by the church showed its roof had been hit close to the main cross, scorching the stone facade, and that windows had been broken.
Father Gabriele Romanelli, an Argentine who used to regularly update the late Pope Francis about the Israeli-Palestinian conflict, was lightly injured in the attack.
TV footage showed him sitting receiving treatment at Al-Ahly Hospital in Gaza, with a bandage around his lower right leg.
"The attacks against the civilian population that Israel has been carrying out for months are unacceptable. No military action can justify such an attitude," Italian Prime Minister Giorgia Meloni said in a statement.
Pope Leo was "deeply saddened" by the loss of life and renewed his appeal for an immediate ceasefire, the Vatican said.
The Israel Defence Forces said it was aware of reports of casualties and was reviewing the incident, adding it made "every feasible effort to mitigate harm to civilians and civilian structures, including religious sites, and regrets any damage caused to them".
Israel has been trying to eradicate Hamas in Gaza in a military campaign that began after the group's deadly attack on Israel in October 2023 and has caused widespread hunger and privation in the tiny enclave.
Palestinian medics said one air strike on Thursday had killed a man, his wife and their five children in Jabalia in northern Gaza, and another in the north had killed eight men who had been handed responsibility for protecting aid trucks.
Three people were killed in an air strike in central Gaza and four in Zeitoun in eastern Gaza, medics said.
Arab mediators Qatar and Egypt, backed by the United States, have hosted more than 10 days of talks on a proposed US 60-day truce.
As part of the potential deal, 10 hostages held in Gaza would be returned along with the bodies of 18 others, spread out over 60 days.
In exchange, Israel would release detained Palestinians. The exact number is not clear.
On Wednesday, US President Donald Trump's Middle East envoy, Steve Witkoff, said that negotiations for a ceasefire in Gaza were going well.
A Palestinian official close to the talks said such optimistic comments were "empty of substance".
Israel's campaign in Gaza has killed more than 58,000 Palestinians, according to Gaza health authorities.
Almost 1650 Israelis and foreign nationals have been killed as a result of the conflict, including 1200 killed in the October 7, 2023, Hamas attack, according to Israeli tallies.
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