UK MP Layla Moran says her relatives are among hundreds of civilians trapped in a Catholic Church in Gaza City as Israeli forces operate nearby.
The Liberal Democrat says her family are "days away from dying" without access to water or food.
The Latin Patriarchate of Jerusalem say a mother and daughter were killed inside the Holy Family Church complex on Saturday by sniper fire.
The IDF said it found no evidence to show the incident took place.
In a statement, the Israel Defense Forces said: "During the dialogue between the IDF and representatives of the community, no reports of a hit on the church, nor civilians being injured or killed, were raised.
"A review of the IDF's operational findings support this."
The Latin Patriarchate of Jerusalem said two Christian women - named as Nahida and her daughter Samar - were shot and killed while walking to a building in the church complex known as the Sister's Convent.
"One was killed as she tried to carry the other to safety," a statement said. Seven more people were shot and wounded as they "tried to protect others inside the church compound" on Saturday.
The patriarchate said no warning had been given and added: "They were shot in cold blood inside the premises of the parish, where there are no belligerents."
The patriarchate said that earlier on Saturday an Israeli tank fired on part of the church compound with 54 disabled people inside. It caused a fire that destroyed the building's generator, the only source of electricity, and some of the disabled people can no longer use their respirators, the statement said.
Members of Ms Moran's extended family - a grandmother, her son, his wife and their 11-year-old twins - are Christian Palestinians who sought refuge inside the church after their home was bombed in the first week of the war.
They have been staying on mattresses along with dozens of others in rooms in the Holy Family Church for more than 60 days.
"I'm now no longer sure they are going to survive until Christmas," Ms Moran told the OceanNewsUK.
They have been keeping in touch with Ms Moran and other family members sporadically through WhatsApp messages and calls - though they have no internet and power is intermittent.
A sixth member of the family - a grandfather - died last month after not being able to get to hospital to receive medical treatment, Ms Moran says.
The five remaining members say they now no longer have access to food or water, and the last remaining generator - which was pumping water from wherever they could get it - has stopped working in the church.
They say soldiers entered the church compound in the last 24 hours and took over a room in a building.
Earlier in the week, the family heard shots being fired and saw bullet casings in the church compound. They say two men were killed on Tuesday while they were coming and going from the building - a bin collector and a janitor.
The family have sent a photo, seen by the OceanNewsUK, of two bodies lying on a street outside the church building. Ms Moran's relatives say the bodies have been decaying outside for days. The OceanNewsUK has not verified the circumstances of what the image shows.
Ms Moran says there has been no explanation as to why Israeli soldiers would target the church and no warnings or leaflets were sent to people sheltering there.
"It does feel like it's making a mockery of keeping civilians safe," Ms Moran adds.
Israel says it is carrying out military operations in Gaza to "eradicate" Hamas and rescue hostages taken by the group.
Early on in the war Israel told people in northern Gaza to move to southern Gaza for their safety. It has also paused military activity in some areas for short periods to allow people to leave. There was also a temporary ceasefire between Israel and Hamas to allow a swap of some Israeli hostages and Palestinian prisoners.
However Israel has also bombed southern Gaza, where it told people to go, and a large number of Palestinians have remained in Gaza City and other northern areas.
Ms Moran says she has been in touch with a number of countries about getting her relatives out of Gaza, but the situation is "incredibly complex".
She adds that the family have considered trying to travel to Rafah in southern Gaza near the border with Egypt but say it is too dangerous while no ceasefire is in place.
Hamas broke through Israel's heavily guarded perimeter on 7 October, killing 1,200 people and taking 240 hostages - some of whom were released during the brief truce.
The health ministry in Gaza, which is run by Hamas, says more than 18,700 people have been killed and 50,000 injured in the enclave since the start of the Gaza war.
