Israel's military said it was assessing the claim, while relatives said they were "waiting for the news to be confirmed or hopefully refuted soon" about the family members, who have become leading faces of the hostage crisis.
“During the Hamas massacre of October 7, the Bibas family, including 10-month-old Kfir Bibas, his 4-year-old brother Ariel Bibas, and their mother Shiri Bibas — were kidnapped alive into Gaza,” the Israel Defense Forces said in a statement.
“The barbarism and cruelty of Hamas is on full display to the world. IDF representatives spoke with the Bibas family following the recent reports and are with them at this difficult time. The IDF is assessing the accuracy of the information,” it added.
It follows a claim by the military wing of Hamas, which said earlier in the day that the three hostages had been killed in Gaza as the result of Israeli bombing.
NBC News could not verify the claim. Israel has accused Hamas of using civilians as human shields.
"Our family is updated on the latest Hamas publication. We are waiting for the news to be confirmed or hopefully refuted soon by military officials," said the Bibas family in a statement released by the Hostages and Missing Families Forum.
It added: "We thank the people of Israel for the warm embrace but ask to maintain our privacy at this complex time."
Footage of Shiri Bibas being kidnapped from kibbutz Nir Oz near the Gaza border as she clutched her two young children has become one of the lasting images of the terror attack, and the subsequent plight of the hostages inside Gaza.
At 10-months old, Kfir is believed to be the youngest captive.
Shiri Bibas’ husband, Yarden, was kidnapped alongside her and their children, but there was no information immediately available about his well-being.
On Tuesday, the Israeli prime minister’s office said that Hamas had claimed not to be holding the mother and two children, saying it had handed them over to another group. The presence of other armed militant groups inside Gaza who are thought to be holding hostages has added to the complexity of negotiations.
The claim about the status of the Bibas family came as talks were going on in Qatar to extend the truce between Israel and Hamas in order to allow for the release of more hostages and Palestinian prisoners.
It also came just hours after relatives led a gathering in central Tel Aviv in an effort to show support and raise awareness about the family's case after they were not among any of the hostages freed since the truce first came into effect last week.
“It’s like a shot in the chest every time that their names are not in the list,” Yarden Bibas’ sister, Ofri, told NBC News at the square where the event was held Tuesday.
Among the hundreds of attendees, including people from the family’s kibbutz, some wore T-shirts with a picture of the family. The word “kidnapped” was stamped in bold letters above the photo.
Orange balloons were released to honor the boys’ red hair and as a symbol of the liberation the family had been denied.
“These two young little redheads really got in the hearts of everybody in Israel and also in the entire world,” Ofri Bibas said.
She called the last seven weeks a “nightmare” but said she hoped the gathering would help push for an extension of the truce.