“The bodies of both are still in the custody of Hamas,” the community said, without elaborating.
The couple were among some 250 people taken hostage from Israeli border communities and military posts.
More than 100 of those abducted have since been freed, many exchanged for Palestinian prisoners.
Israel says 129 captives are still missing in Gaza, including 23 believed to have been killed.
Three hostages were mistakenly shot dead by soldiers in Gaza, according to the Israeli army.
“There are no words to describe the pain of losing our parents and grandparents to the massacre that took place on our kibbutz,” the family of Haggai said in a statement.
“We pray that their bodies … will be soon returned to us, and that their murders are a reminder for leaders everywhere to bring the hostages home now before it is too late.”
Israel PM visits Gaza vows to ‘intensify’ fighting; heckled by hostage families
Israel PM visits Gaza vows to ‘intensify’ fighting; heckled by hostage families
Ahl Haggai, the couple’s son, has said that in a final phone call on October 7, his mother had told a paramedic that she and her husband had both been wounded.
“The only evidence we have … is a video of my dad on the back of a truck, laying down injured,” he told Agence France-Presse earlier this month.
“She’s nowhere to be found,” he said, with only his mother’s glasses recovered from the kibbutz.
In a statement on Thursday, US President Joe Biden said: “This tragic development cuts deep, coming on the heels of last week’s news that Judith’s beloved husband, Gad Haggai, is believed to have been killed by Hamas.”
Working while on holiday in the US Virgin Islands, Biden said he would never forget what the couple’s daughter and the family members of other Americans held hostage in Gaza told him when he met them this month.
“They have been living through hell for weeks. No family should have to endure such an ordeal. And I reaffirm the pledge we have made to all the families of those still held hostage: we will not stop working to bring them home,” Biden said.
Biden and national security adviser Jake Sullivan have been deeply engaged on the hostage issue, according to administration officials. Biden has spoken numerous times to Israeli Prime Minister Benjamin Netanyahu and the emir of Qatar on securing their release.
Israelis have held frequent rallies to highlight the plight of the remaining hostages and put pressure on the authorities to secure their release, with hundreds marching to parliament on Thursday.
“Bring them home!” they chanted outside the assembly in Jerusalem, an Agence France-Presse journalist reported.
“All I can hope is that as many people (as possible) will remain alive,” Nikki Littman, 55, who took part in the rally, said.
“I don’t trust the government. I don’t trust Hamas. I fear Hamas. I fear our existence here,” said Littman, who teaches Japanese at a university.
The October 7 Hamas attack resulted in the deaths of around 1,140 people in Israel, most of them civilians, according to an Agence France-Presse tally based on the latest official Israeli figures.
Israel’s relentless offensive on Gaza has since killed 21,320 people, mostly civilians, according to the latest toll from the health ministry in the Hamas-run territory.