"Around noon (1000 GMT) today... a sniper of the IDF (Israeli army) murdered two Christian women inside the Holy Family Parish in Gaza," where Christian families have been sheltering since the Israel-Hamas war broke out, the patriarchate said in a statement.
"Nahida and her daughter Samar were shot and killed as they walked to the Sister's Convent. One was killed as she tried to carry the other to safety," it added, without specifying the victims' ages.
Seven more people were wounded by gunfire as they tried to protect others, the statement said.
The Israeli army did not immediately respond to a request for comment about the incident on the grounds of the Gaza Strip's only Catholic church.
The patriarchate said no warning was given before the shooting started, adding: "They were shot in cold blood inside the premises of the Parish, where there are no belligerents."
The war in Gaza was triggered by Hamas's unprecedented October 7 attack on Israel, which killed around 1,140 people, most of them civilians, according to official figures.
Israel's campaign to crush the militant group has so far killed at least 18,800, mostly women and children, according to the territory's Hamas-run health ministry.
