Prime Minister Benjamin Netanyahu expressed regret after Israeli tank fire killed three people at a Catholic church in Gaza on Thursday, blaming a "stray" round for the deaths after a phone call with US President Donald Trump.

The Latin Patriarchate of Jerusalem said 10 others were also wounded in the attack on the Holy Family Church in Gaza City – the territory's only Catholic house of worship – including parish priest Father Gabriel Romanelli.

Witnesses and the Latin Patriarch said a tank shell slammed directly into the church around 10:30am (0730 GMT), but the Israeli military later said an initial inquiry "suggests that fragments from a shell... hit the church mistakenly".

Pope Leo XIV said he was "deeply saddened" by the loss of life at Holy Family, which the late Pope Francis had kept in regular contact with throughout the war between Israel and Hamas militants.

Israel's military maintained it made "every feasible effort to mitigate harm to civilians and religious structures," while Netanyahu promised an investigation.

"Israel deeply regrets that a stray ammunition hit Gaza's Holy Family Church. Every innocent life lost is a tragedy," Netanyahu said in a statement.

White House Press Secretary Karoline Leavitt said Trump had called Netanyahu after having "not a positive reaction" to news of the strike.

"It was a mistake by the Israelis to hit that Catholic church, that's what the prime minister relayed to the president," she said. (AFP)