Shortly before the final release of women and children hostages scheduled under the truce, the military wing of Hamas said the youngest hostage - baby Kfir Bibas - had been killed in an earlier Israeli bombing, along with his four-year-old brother Ariel and their mother.
Their father has also been held.
The Israeli military said it was checking the claim, which was potentially explosive, as the family were among the highest-profile civilian hostages yet to be freed.
"Hamas is wholly responsible for the security of all hostages in the Gaza Strip," the army said in a statement.
Reuters could not independently confirm the Hamas statement.
Relatives had issued a special appeal for the family's freedom after the children and their parents were excluded from the penultimate group freed on Tuesday.
The family of Kfir Bibas are among the highest-profile Israeli civilian hostages yet to be freed. (AP PHOTO)
Families of the Israeli hostages due to be released later on Wednesday were informed earlier of their names, the final group to be freed under the truce unless negotiators succeed in extending it.
Officials did not say at the time whether that included the Bibas family.
Gaza's Hamas rulers published a list of 15 women and 15 teenagers to be released from Israeli jails in return for the hostages, among the 240 people seized by Hamas fighters in their deadly raid on Israel on October 7.
For the first time since the truce began, the list of Palestinians to be freed included Palestinian citizens of Israel as well as residents of occupied territory.
A Palestinian official earlier told Reuters that despite a willingness on both sides to prolong the truce, no agreement had yet been reached.
Discussions were still under way with mediators Egypt and Qatar, the official said.
Israeli government spokesman Eylon Levy said Israel would consider any serious proposal.
"We are doing everything we can in order to get those hostages out. Nothing is confirmed until it is confirmed," Levy told reporters in Tel Aviv.
"We're talking about very sensitive negotiations in which human lives hang in the balance."
Once the release of hostages ends, the fighting will resume, he said: "This war will end with the end of Hamas."
