"We demand to abandon the Witkoff framework and return to the Trump framework – all together or unleash hell on Hamas," the Tikva Forum said in a statement.
This comes as the 42-day hostage-ceasefire deal expired on March 1, with Israel saying it is ready implement US envoy Steve Witkoff's proposal.
Albag stated that the five will finish their rehabilitation, after which they will be discharged from military service.
Mantzur, 85, from Kissufim, was the oldest hostage held in Hamas captivity. His body was returned to Israel in February.
Asked on Saturday whether he had watched Sharabi's testimony on Channel 12's Uvda, Barkat said "I had more important things to do."
An Israeli official noted that the move came in full coordination with the Trump administration.
Sharabi is set to fly to Washington on Monday and his meeting with the US president is scheduled for Tuesday, Sharabi's brother said.
The family said it had identified Cohen, whose face is blurred, via a tattoo that appeared on his arm.
After his interview with Channel 12's Uvda, everyone should be listening to Eli Sharabi.
On the first day of the framework, half of the living hostages and the remains of deceased hostages will be released.