The group did not release the names of those said to be killed, but the video showed what appeared to be three unidentifiable corpses using censor bars over their faces.
“Your captives will not be released unless our prisoners are freed,” the video added.
Israel rescued four captives held by Hamas in a deadly operation in central Gaza’s al-Nuseirat refugee camp.
Shortly after Hamas initially stated Israeli forces had killed some of the captives on Saturday, an Israeli military spokesman claimed the news was a “blatant lie”.
The Palestinian death toll from the operation was worst of any other 24-hour period of the Gaza war for months and included many women and children, Palestinian medics confirmed.