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Hamas said it could agree to a Qatar-mediated deal for the release of 100 Israeli hostages in return for 200 Palestinian children and 75 women being held in Israeli prisons.
Abu Obeida, spokesman for the group’s military wing, also said a ceasefire and an influx of humanitarian aid would have to be part of the deal.
"We informed the mediators we could release the hostages if we obtained five days of truce ... and passage of aid to all of our people throughout the Gaza Strip but the enemy [Israel] is procrastinating," Mr Obeida said in an audio statement late on Monday.
"The truce should include a complete ceasefire and allow aid and humanitarian relief everywhere in the Gaza Strip.”
Qatar, alongside Egypt, has been meditating hostage release talks between Israel and Hamas.
Israeli leaders have so far insisted there will be no broader ceasefire until hostages are released from Gaza.
US President Joe Biden on Monday spoke to Sheikh Tamim, Emir of Qatar, about “the urgent ongoing efforts to secure additional releases”.
Mr Biden said he was "somewhat hopeful" the Qatar-mediated talks could lead to a deal.
The White House said Mr Biden thanked Qatar and Sheikh Tamim personally for earlier efforts to secure the release of hostages from Hamas, including two US citizens.
A statement said the emir "condemned unequivocally the holding of hostages by Hamas, including many young children, one of whom is a three-year old American citizen toddler, whose parents were killed by Hamas on October 7.
"The two leaders agreed that all hostages must be released without further delay."
An Israeli official told The Washington Post a temporary ceasefire of about five days could accompany the exchange of hostages and prisoners.
“The agreement could be announced within days if final details are resolved,” the Israeli official was quoted as saying.