Israel didn't send delegate, so they are pointing the finger at the US because the US was their proxy.
Since these negotiations go on behind closed doors, it's up to the reader to read the tea leaves. Sounds like smoke and mirrors.
The NY Times article that you posted is from May 6, 2024 at May 6, 2024, 9:13 p.m. ET. More recent article from NY Times below is from May 7, 2024, 12:12 a.m.mentions 40 hostages.
snips for emphasis
Hamas’s Offer to Hand Over 33 Hostages Includes Some Who Are Dead
May 7, 2024, 12:12 a.m. ET
The Israelis initially wanted 40 to be released in the first phase but came to understand that Hamas did not hold that many who fit the criteria. Israeli and American officials have long assumed that some of the hostages may be dead.
Israel has agreed to send a delegation to review the proposal and contemplate further concessions.
https://archive.ph/Ktekn#selection-473.0-473.65
A failure to release 33 living hostages would appear to conflict with Israeli demands.
Israel had initially demanded that 40 living hostages of the 132 still in Gaza be released in the first phase of the three-phase plan — all of them in the so-called “humanitarian” category: women, children, elderly and sick people.
According to multiple reports, it then agreed to lower that number to 33 after Hamas said it did not hold enough living individuals in the category.
However, the claim that even the 33 under discussion are not all alive appears to be a new walk-back by the terror group.
Hamas officials claimed Monday evening that the deal would yield an end to the war, whereas
Israel has said repeatedly that it will not accept an agreement that involves ending the war and that it fully intends to resume its campaign to destroy Hamas once any deal has been carried out.
https://www.timesofisrael.com/hamas-says-33-hostages-to-be-freed-in-1st-phase-of-a-deal-not-all-necessarily-alive/
US and everyone else is really against the Rafah invasion. Israel is pretty adamant that it will go forward.
US concerns over Israel’s Gaza policy led to weapons holdup
The Biden administration is holding up shipments of two types of Boeing-made precision bombs to send a political message to Israel, according to a U.S. official and six other people with knowledge of the deliberations.
The U.S. has yet to sign off on a pending sale of Boeing’s Joint Direct Attack Munitions — both the munitions and kits that convert them to smart weapons — and Small Diameter Bombs, according to six industry and congressional sources with knowledge of the discussions.
While the Biden administration has not formally denied the potential sale, it is essentially taking action through inaction — holding off on approvals and other aspects of the weapons transfer process — to send a message to Israel, a U.S. administration official familiar with the process told POLITICO. The official, along with others, was granted anonymity to discuss sensitive internal deliberations.
This appears to be the first time the U.S. administration has delayed a potential weapons sale for Israel since Hamas attacked the country on Oct. 7. President Joe Biden has been under pressure from some in his party to set conditions on aid to Israel after the Israeli bombing campaign in Gaza began to exact a heavy toll on civilians, and after Israel hit humanitarian convoys delivering aid to the enclave.
https://www.politico.com/news/2024/05/07/us-concerns-over-israels-gaza-policy-led-to-weapons-holdup-00156528
Israelis frustrated with U.S. handling of hostage talks
Israeli officials claim the Biden administration knew about the latest hostage and ceasefire deal proposal Egypt and Qatar negotiated with Hamas, but didn't brief Israel before Hamas announced it accepted it on Monday. A senior U.S. official pushed back saying "American diplomats have been engaged with Israeli counterparts. There have been no surprises."
Why it matters: The episode has created deep disappointment and suspicion among senior Israeli officials regarding the U.S. role in the hostage deal talks and could negatively influence the negotiations going forward.
The U.S. official said "this is an extremely difficult process with negotiations conducted through intermediaries in Doha and Cairo."
He added that the U.S. believes Israel has engaged in the talks in good faith and that Israel's late April proposal was "the most forward leaning proposal to date. To secure a ceasefire, Hamas simply needs to release hostages. It's all mapped out."
The official also said the Biden administration sees Hamas' response as a counter-proposal and not as a new proposal.
Behind the scenes: Three Israeli officials said the Hamas announcement on Monday surprised the Israeli government and that Israel didn't receive the text of the group's response from the mediators until an hour after Hamas released its statement.
https://www.axios.com/2024/05/07/us-israel-hamas-hostage-ceasefire-talks
Arab diplomat: Repeated Israeli refusal to dispatch negotiating team has harmed hostage talks
Israel’s repeated refusal to send a negotiating team to meet with mediators has hampered efforts to secure a hostage deal, an Arab diplomat tells The Times of Israel.
The mediators had wanted Israel to dispatch a delegation to Cairo over the weekend when CIA chief Bill Burns was in town and the mediators were gearing up for Hamas’s official response to the latest proposal, the diplomat says, claiming Israel’s absence led it to be being out of the loop.
Following Hamas’s Monday response, Israel sent a lower-level negotiating team to Cairo, while officials in Jerusalem surmised that the terror group’s latest proposal brought the parties back to square one.
He declines to elaborate but doesn’t deny the suggestion that Prime Minister Benjamin Netanyahu has refused to dispatch negotiating teams due to pressure from far-right coalition partners who want him to take a tougher stance in the talks. Other war cabinet ministers, including National Unity chairman Benny Gantz and his deputy Gadi Eisenkot, have argued that Israel should always show willingness to hold talks, while sticking to guiding principles once the negotiating team is in the room.
https://www.timesofisrael.com/liveblog-may-7-2024/
Netanyahu: Hamas offer aimed at ‘sabotaging’ Rafah op, is ‘very far’ from Israeli demands
Prime Minister Benjamin Netanyahu says that the latest Hamas proposal for a ceasefire deal was “meant to sabotage the entry of our forces into Rafah.”
“That did not happen,” the premier says in a video statement.
The Rafah operation is meant to bring back the hostages and to eliminate Hamas, says Netanyahu. “We already proved in the previous hostage release — military pressure on Hamas is a precondition for the return of the hostages.”
He emphasizes that the Hamas offer is “very far from Israel’s vital demands.”
“Israel will not allow Hamas to restore its wicked rule in the Strip,” he promises. “Israel will not allow it to rehabilitate its military capabilities in order to keep working toward our destruction.”
https://www.timesofisrael.com/liveblog_entry/netanyahu-hamas-offer-aimed-at-sabotaging-rafah-op-is-very-far-from-israeli-demands/
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