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

Over 40 projectiles have been launched from Lebanon across Israel's northern border toward the Galilee and Golan Heights area since Thursday morning, Israeli military officials told ABC News.

Two people were hit by shrapnel and wounded in the Golan Heights, according to Israeli Emergency Services.

The Israel Defense Forces said military exercises are continuing in the north to increase readiness.

-ABC News’ Dana Savir, Jordana Miller, Tom Soufi Burridge and Hugo Leenhardt

Hamas’ new demands in response to the latest cease-fire proposal include an insistence that the timetable be moved up for the withdrawal of Israeli troops from all Gazan territory, according to a U.S. official with knowledge of the negotiations.

The official also said that Hamas communicated additional demands for assurances that a lasting cease-fire would be achieved that were not included in the previous version of the agreement.

In the first days of May, Hamas seemingly accepted a hostage deal presented by Qatar and Egypt, only for Israel to say it had not signed off on that draft, sparking mass confusion. Later, Israel did say it would return to the negotiating table, which eventually led to the formation of the proposal on the table.

-ABC News’ Shannon Crawford

Secretary of State Antony Blinken on Wednesday weighed in on Hamas’ official response to the cease-fire proposal, stressing that a deal is the "single, most effective way" to alleviate civilian suffering and avoid escalation in the region.

“Hamas has proposed numerous changes to the proposal that is on the table," Blinken said at a news conference in Qatar with Qatari officials. "We discussed those changes with Egyptian colleagues, and today with the prime minister [of Qatar]. Some of the changes are workable, some are not."

"Here, in a nutshell is where we stand," Blinken said. "Hamas could have answered with a single word: yes. Instead, Hamas waited nearly two weeks and then proposed more changes, a number of which go beyond positions it had previously taken and accepted."

Blinken said that as a result "the war Hamas started will go on," but that "in the days ahead, we’re going to continue to push on an urgent basis" to "try to close this deal."

Blinken noted that almost everyone he’s spoken with during his eight trips to the Middle East since Oct. 7 made clear they wanted to see a negotiated solution to the conflict.

"I cannot speak for Hamas or answer for Hamas and ultimately, it may not be the path Hamas wants to pursue. But Hamas cannot and will not be allowed to decide the future for this region and its people," he said.

Blinken was pressed on whether the deal was salvageable and whether more pressure needed to be applied to Israel. The secretary declined to characterize Hamas’ response as a rejection, as Israeli officials have, but expressed significant skepticism.

"At some point in a negotiation, and this has gone back and forth for a long time, you get to a point where if one side continues to change its demands, including making demands and insisting on changes for things that it already accepted, you have to question whether they’re proceeding in good faith or not," he said.

Blinken went on to say he believes the gaps are bridgeable, but "it doesn’t mean they will be bridged" because it depends "on people saying yes."

"Hamas had this for 12 days. ... People were suffering throughout those 12 days. The longer this goes on, the more people will suffer," he asserted. "It’s time for the haggling to stop."

Blinken was also adamant that Israel was not the problem.

"Look, Israel accepted the proposal as it was and as it is. Hamas didn’t. So I think it’s pretty clear what needs to happen," he said.

-ABC News’ Shannon Crawford