Abu Obeida, spokesman for the Ezzedine Al-Qassam Brigades, said in a statement: "In two separate incidents, two (Hamas) soldiers 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.

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

Palestinian resistance members seized 251 captives at the start of the Israeli war on Gaza, with 111 of them still held in the Strip including 39 the Israeli army says are dead.

The Israeli occupation army had previously killed no less than 16 captives accidentally in attacks on the Palestinian territory. 

Israel and Hamas have been negotiating a ceasefire and captive deal for months, although the deal is being sabotaged by the increasing demands of Israeli Prime Minister Benjamin Netanyahu. 

Hamas on Sunday called on US, Qatari and Egyptian mediators to implement a ceasefire plan for Gaza put forward by US President Joe Biden, instead of holding "more talks" which allows Tel Aviv to "continue its genocidal war against the Palestinian people."

International mediators had invited Israel and Hamas to resume talks toward a long-sought truce and captive-release deal after the fighting in Gaza and the Israeli assassinations of Hamas and Hezbollah leaders sparked fears of a wider conflict.

The obstacle named Netanyahu

Netanyahu, who has consistently refused to sign ceasefire agreements, accepted an invitation from the United States, Qatar, and Egypt for talks scheduled for Thursday. However, on Saturday, his army carried out a new massacre, killing around 100 Palestinians who were sheltering in Al-Tab'een School, in the Al-Daraj neighbourhood in Gaza City.

On Sunday, Hamas said it wanted the implementation of a truce plan laid out by Biden on 31 May and later endorsed by the UN Security Council, "rather than going through more negotiation rounds or new proposals that provide cover for the occupation's aggression and give it more time to perpetuate the genocide war against the Palestinians."

Unveiling the plan, Biden had called it a three-phase "roadmap to an enduring ceasefire and the release of all hostages", and said it was an Israeli proposal.

Israel's war on the Gaza Strip since then has killed at least 39,897 people, mostly women and children. 

Netanyahu and his Defence Minister Yoav Gallant exchanged criticism over the stalled talks.

"The reason a captive deal is stalling is in part because of Israel", Israeli media, including television channel Kan, reported Gallant saying in a private briefing for a parliamentary committee on Monday.

Gallant was discussing the choice Israel faced between a ceasefire deal that could end the war in Gaza and in the north with Lebanese Hezbollah, Kan reported.

"I and the defence establishment support the first option," he said, rather than talk of "'total victory' and all that nonsense", a phrase frequently used by Netanyahu in his communications.

Within hours of Gallant's words leaking to the media, Netanyahu hit back in a statement issued by his office, accusing Gallant of endangering a deal to secure the release of Israelis detained in Gaza.

"When Gallant adopts the anti-Israel narrative, he harms the chances of reaching a captive release deal," Netanyahu said, claiming that Hamas supremo Yahya Sinwar is the one "who has been and remains the only obstacle."

Hamas commented on the row between the two politicians, with one of its leaders, Izzat al-Rishq saying in a statement that "Gallant's admission (...) confirms what we have always said."

"Netanyahu is lying to the world and to captive families, he doesn't care about the captive' lives and doesn't want to reach an agreement", he added.

Hamas officials, some analysts and critics in Israel have said Netanyahu has sought to prolong the fighting for political gain.

In late July, Israeli media reported that Gallant was criticising the lack of a deal to guarantee the return of the detainees held in Gaza.