The armed wing of Palestinian group Hamas said on Monday its militants had shot and killed an Israeli hostage and wounded two others, both women, in two separate incidents in Gaza.

Palestinian militants seized 251 hostages during their October 7 attack on Israel that triggered the ongoing war, with 111 of them still held in Gaza, including 39 the Israeli military says are dead.

Abu Obeida, spokesman for the Ezzedine Al-Qassam Brigades, said in a statement: "In two separate incidents, two recruits assigned to guard enemy prisoners fired at a Zionist prisoner, killing him immediately, and also injured two female prisoners critically."

The statement, posted on Telegram, did not identify the hostages or say when or where the incidents occurred, but noted "attempts are being made to save the lives" of the two women.

Abu Obeida said Hamas had formed a committee to investigate the shootings.

The Israeli military said in a statement that it does "not have any intelligence information that allows us to refute or confirm Hamas' claims."

"We will continue to examine and verify the credibility of the message," the statement added.

Israeli military spokesman Rear Admiral Daniel Hagari, in a televised briefing earlier on Monday, said: "We do not forget for a moment the hostages being cruelly held by Hamas in Gaza."

"We are deeply concerned about their physical and mental condition, given the prolonged time that has passed and the harsh conditions of their captivity."

The October 7 attack resulted in the deaths of 1,198 people, mostly civilians, according to a tally based on official Israeli figures.

Israel's retaliatory military offensive in the Gaza Strip since then has killed at least 39,897 people, according to the Hamas-run territory's health ministry, which does not provide details on civilian and militant deaths. (AFP)