Hamas Israeli Government Release of Israeli Hostages Qatar Israel Release of Hostages Hamas Demands Egypt US Involvement Official Statements Agreement Qatar Mediation Humanitarian Aid Delivery Cease-fire Agreements Palestinian Terrorists Release of Palestinian Women and Children List Evaluation Bangkok Solution Medicine Delivery Mediation Ceasefire Negotiation Principles War Cabinet Prisoner Release United States Gaza Hamas Counterproposal Israeli Hostages Gaza Hostages US Cease-fire Deal Exile Biden-Netanyahu Call Hostage Release Efforts United States' Role Gaza Strip Negotiation Proposals Negotiating Parties Benjamin Netanyahu Cairo Talks Mossad and Shin Bet Bill Burns Joe Biden US Government Stalled Negotiations Gaza Hostage Deal Rafah Invasion Deal with Hamas Details Knowledge of Hostage Location Possible Deal Tentative Agreement Rumors and Reports Release Conditions Number of Hostages