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

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