A snap shot of the video released by Hamas for one of the hostages.
Omri Miran, 47, and Keith Siegel, 64, spoke about their experiences in captivity and their desire to return home.
"I have been here in Hamas captivity for 202 days. The situation here is unpleasant, difficult and there are many bombs," Miran said.
"It's time to reach a deal that will get us out of here safe and healthy... Keep protesting, so that there will be a deal now."
In the video, both men express their awareness of recent demonstrations in Tel Aviv and Jerusalem.
They urge the protesters to persist in their efforts, suggesting that sustained pressure on the government could lead to negotiations.
Saturday's video comes as Hamas says it is studying Israel's latest counterproposal for a Gaza ceasefire after media reports that mediator Egypt had sent a delegation to Israel to jump-start stalled negotiations.
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