State Department spokesperson Matt Miller on Thursday shed little light on the next steps for negotiations toward a cease-fire deal, but dismissed the idea that Israeli Prime Minister Benjamin Netanyahu’s and other Israeli officials’ lack of public enthusiasm for the proposal soured the chances that Hamas would accept it.

"I personally doubt that comments, or lack of comments, from the Israeli government had anything to do with the Hamas response," he said. "We were disappointed both that it took so long to get a response and that the response had a number of changes that could drag the negotiations out further."

Miller was also reticent to discuss remaining sticking points, but on multiple occasions, he dismissed the idea that Hamas should need assurances for a lasting peace, emphasizing that if the proposal were enacted, the cease-fire prescribed under phase one of the deal would last as long as negotiations did.

"At least we would have had a cease-fire. We would have had a halt to the suffering," Miller said. "Hamas didn't do that. Instead, they dragged it out for 12 days, and now there will be continued haggling and delay."

-ABC News’ Shannon Crawford

President Joe Biden said the G7 leaders discussed the Gaza cease-fire and hostage proposal on Thursday.

When asked if he was confident a deal would be reached soon, Biden said, "No." He added, "I haven't lost hope -- but it's going to be tough.”

"Hamas has to move," Biden said.

-ABC News’ Justin Gomez

Israel will not send a delegation for further talks on a cease-fire deal, an Israeli source confirms to ABC News.

The U.S., Egypt and Qatar are still trying to pressure Hamas to return to the outline of a cease-fire deal presented by President Joe Biden.

Hamas in a statement Thursday said they have "demonstrated, in all stages of negotiations to stop the aggression, the required positivity to reach a comprehensive and satisfactory agreement, based on the fair demands of our people for a definitive cessation of aggression, a complete withdrawal [of IDF forces] from the Gaza Strip, the return of the displaced, the reconstruction and a serious prisoner exchange deal."

A "significant portion" of people living in the Gaza Strip are "now facing catastrophic hunger and famine-like conditions," the head of the World Health Organization said, as neighboring Israel continues to restrict supplies of food and other basic necessities to the war-torn enclave.

"Despite reports of increased delivery of food, there is currently no evidence that those who need it most are receiving sufficient quantity and quality of food," WHO Director-General Tedros Adhanom Ghebreyesus said at a press briefing Wednesday.

More than 8,000 children under the age of 5 in Gaza have been diagnosed and treated for acute malnutrition, including 1,600 with severe acute malnutrition. But only two stabilization centers for severely malnourished patients can currently operate in Gaza due to insecurity and lack of access, according to Tedros.

At least 32 deaths in Gaza since the war with Israel began on Oct. 7 have been attributed to malnutrition, including 28 among children under 5 years old, Tedros said.

More than 1 million people in Gaza -- half of the territory's population -- are "expected to face death and starvation by the middle of July," according to the most senior official dedicated to humanitarian affairs at the United Nations.

-ABC News’ Morgan Winsor

National security adviser Jake Sullivan said the U.S. will work with Egypt and Qatar to "bridge final gaps" on cease-fire negotiations that are consistent with President Joe Biden’s May 31 speech and consistent with the U.N. Security Council Resolution.

"Many of the proposed changes are minor and not unanticipated, others differ more substantively from what was outlined in the U.N. Security Council resolution," Sullivan told reporters.

Sullivan said their goal is "to bring this process to a conclusion."

"Our view is that the time for haggling is over, it's time for a cease-fire to begin and for the hostages to come home," he said.

-ABC News’ Justin Ryan Gomez