Hostage Release Hamas Hostage Situation Hamas Response Humanitarian Aid Release of Hostages US Involvement Benjamin Netanyahu Hostages Israeli Hostages Tactical Pauses Opposition to Ceasefire Humanitarian Pauses U.S. Involvement Truce Extension Hamas Leadership Hamas Leaders Hostage Deal Hamas Rejection Israeli Offer Hostage Exchange Exchange of Prisoners Truce Proposal Paris Discussions Proposed Deal Qatari and Egyptian Mediation Israeli Government Hamas Officials Gaza Hostage Deal Release of Political Prisoners Biden Administration's Initiative Hamas Counterproposal Netanyahu's Stance Hamas's Terms Israeli Response Negotiation Process Humanitarian Situation Hamas Counteroffer Future Outlook Diplomatic Efforts Truce Hamas Offer Hamas Ceasefire Proposal Rafah Offensive Gaza Hostages Mediators Negotiation Challenges Hostage Talks Egypt Failure of Ceasefire Talks Ceasefire Proposal Hamas Demands US Policy Hamas Hostages Government Positions Mediation Efforts Conditions Aid for Palestinians Viability Assessment