The statement came out after negotiators met in Doha on Thursday and Friday in the latest round of ceasefire talks.
Qatar's PM warned Iran that an attack could endanger diplomatic efforts to reach a ceasefire-hostage deal.
A source in the Israeli negotiating team said that Netanyahu has allowed significant leeway on a few of the substantial disputes.
Finance minister doubles down on opposition to hostage deal: "Surrender agreement with Sinwar is bad for Israel and endangers its security."
Mediators, including the US, reportedly expressed support for Barghouti's release.
Hezbollah drone attack wounds 19 | IDF kills Hamas weapons smuggler | US soldiers wounded in Iraq | International leaders meet to discuss escalation in Middle East
Smotritch, Ben-Gvir may face US sanctions • Houthis damage cargo ship in Gulf of Aden • IDF and Palestinians reportedly clash near Hebron •
Bibi accused of sabotaging hostage deal • IDF destroys Hamas tunnels in Rafah • Groups protest Netanyahu's trip to Congress
Hamas official Izzat El-Reshiq accused Israel of trying to derail efforts by mediating countries Egypt and Qatar to reach an agreement by stepping up its attacks in the enclave.
The assassination of Mohammad Deif, which has yet to be confirmed, could change the balance of the course of war and hostage negotiations a former Shin Bet official argues.