The footage shows Gadi Moses, 79, and Gadi Katzir, 47, speaking in front of a camera, asking the Israeli government to arrange their release.
It is not clear when or where the clips were filmed.
In the video, Moses asks Israeli Prime Minister Benjamin Netanyahu, Defense Minister Yoav Gallant, war cabinet member Benny Gantz and Israel Defense Forces Chief of Staff Herzi Halevi to make every effort to return them to their families.
Katzir makes similar remarks, asking the government to make an exchange deal with Islamic Jihad.
Both men speak about the dangers they are facing.
“We do not want to die in Gaza. Our lives here are extremely dangerous. And we want everything necessary to be done, in order to bring us back home,” Katzir says.
Moses was taken alongside his ex-wife Margalit Moses, who was released during the truce on November 24.
Katzir’s father, Rami, was killed on October 7, and his mother, Hanna, was abducted and then released as part of the truce.
Hamas’ military wing, the Qassam Brigades, released a video on Monday showing three Israeli male hostages in captivity in Gaza.