Video shows US and Israeli hostages alive in Gaza
Mr Siegel, a US citizen, was kidnapped with his wife Aviva on 7 October.
She was freed in November during a brief truce.
Earlier this month, she told the BBC how the couple had at one point been left in a tunnel by their captors as they were moved from place to place.
At the time, she said, she did not know if Keith was still alive.
The Hostages Families Forum Headquarters said the Siegel and Miran families were aware of the latest video.
It said the proof the two were alive was “the clearest evidence that the Israeli government must do everything to approve a deal for the return of all the hostages”.
It follows another proof-of-life video the group released earlier this week, showing Israeli-American hostage Hersh Goldberg-Polin, 23, who is shown without his lower left arm in the short clip. It was blown off during Hamas’s 7 October attack on southern Israel.
