The group has often attributed previous killings of hostages to Israeli bombardment.
Israeli Army spokesman Avichay Adraee said in Arabic on X: “In the last few minutes, the terrorist Hamas published a written report claiming that in two separate incidents, Hamas activists killed an Israeli captive and wounded two women captives. At this stage there is no intelligence document to confirm or refute Hamas’ allegations. We continue to investigate the credibility of the statement and will provide information where we have it.”
Earlier, the Palestinian group named Gaza leader Yahya Sinwar as its new leader following the assassination of former leader Ismail Haniyeh in Tehran on July 31.
On Saturday, an Israeli air strike on a Gaza City school compound housing displaced Palestinian families killed about 100 people.
Israel on Monday said 31 militants were among the dead.
Hamas and the Islamic Jihad denied the Israeli allegations, and said no gunmen were present at the school.
There have been conflicting reports about expectations regarding outcomes of talks aiming to end the war in Gaza slated for Thursday.
Hamas on Sunday cast doubt on its participation in the anticipated talks.
A ceasefire deal would aim to end war in the Gaza Strip and ensure the release of Israeli hostages held in the enclave in return for many Palestinians jailed by Israel.
Hamas wants a deal to end the war while Israeli Prime Minister Benjamin Netanyahu says the war would end only after Hamas is eradicated.