Hamas has offered to release half of the remaining living hostages and a number of bodies in exchange for a two-month ceasefire, Palestinian sources told Sky News Arabia.
In addition to demanding a temporary ceasefire, Hamas also conditioned the release on the immediate resumption of aid deliveries.
Hamas also wants strong American guarantees that negotiations to end the war will begin during the temporary ceasefire and that Israel will stop placing conditions and obstacles to the delivery of aid.
The same source indicated that Hamas doubted whether the US was able to compel Prime Minister Benjamin Netanyahu to abide by the terms of any agreement.
The source pointed to the recent release of the last remaining American hostage, Edan Alexander, last week.
Following his release, Hamas had expected that Israel would begin allowing the entry of humanitarian and food aid. However, this didn't happen, and the Trump administration did not pressure Israel either.
Hamas makes additional requests
Hamas also requested that family members of Hamas leadership be allowed to leave the Gaza Strip and that Israel promise not to pursue them.
The source also said that Hamas expressed willingness to give up its weapons after relinquishing control of Gaza.
This comes hours after Netanyahu instructed the negotiating team to "exhaust all efforts" to release the hostages.
Negotiations had stalled for the past three days, a source told The Jerusalem Post, and the same source said that Netanyahu had given the team "freedom of action," after reports had indicated that they had not been given sufficient space to negotiate.
Amichai Stein contributed to this report.