A photo grab from a video released by Hamas shows the three Israeli captives, from left to right: Yossi Sharabi, Itai Svirski and Noa Argamani.
The video showed a woman captive named in Israeli media as Noa Argamani, 26, speaking under duress, revealing that two men she was held captive with had been killed in captivity.
It was not clear when the video was taken.
Hamas released another video on Sunday showing Argamani along with two captives who were seen alive.
The pair, named in Israeli media as Yossi Sharabi, 53, and Itay Svirsky, 38, were the same men announced as having been killed in Monday's video.
In a statement released with Monday's video, Hamas's armed wing, the Ezzedine al-Qassam Brigades, said the two men were killed in "the Zionist army's bombing".
Shortly after the video's release, Israel's defense minister Yoav Gallant told a news conference that Hamas was applying "psychological pressure" to the families of the captives.
The army was helping the families, he said, and keeping them up to date with any developments.
"Hamas has been hit hard by the IDF (military)," he said.
"What's left for it is to touch a sensitive nerve in Israeli society through acts of psychological abuse against the family members."
Ruling out any ceasefire in Gaza, Gallant reiterated that the only way to get the captives back home is by continuing to apply "military pressure".
Otherwise, he said, "nobody will talk to us" and we "will not succeed in reaching any agreements."
* This story was edited by Ahram Online.
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