Israeli Prime Minister Benjamin Netanyahu will likely send negotiators to Cairo in the coming days, an Israeli political source told ABC News.

Egypt and Qatar are co-hosting a new round of negotiations on the proposed hostage and cease-fire deal on Thursday in Cairo, according to Egyptian state TV.

-ABC News' Jordana Miller

Aid organizations are sounding the alarm as Israeli troops advance toward Rafah, the southernmost governorate of the war-torn Gaza Strip, where more than a million people are displaced.

The Norwegian Refugee Council warned Thursday that expanded military operations on overcrowded Rafah would "lead to more civilian deaths and risk the aid system in Gaza coming to a halt."

"An expansion of hostilities could turn Rafah into a zone of bloodshed and destruction that people won't be able to escape. There is nowhere left for people to flee to," Angelita Caredda, regional director for the Middle East and North Africa at the Norwegian Refugee Council, said in a statement. "Conditions in Rafah are already dire, and a full-scale Israeli military operation will lead to even more loss of civilian life. Aid workers have been grappling with insecurity and insufficient aid for months. Attacks in areas where they provide food, water and shelter means this life-saving support will be impeded, if not entirely stopped."

"Repeated relocation orders issued by Israeli authorities over four months of hostilities have forced tens of thousands of people to flee multiple times to areas that are not safe and where shelter is not available," Caredda added. "Palestinians are being pushed into tiny corners, narrow alleys, and overcrowded shelters while residential areas continue to be pounded."

The Israel Defense Forces originally designated some of the relocation areas in Gaza as "safe zones," but they have been heavily bombarded, according to the Norwegian Refugee Council. The United Nations estimates that 67% of the coastal enclave, or 246 square kilometres, has been placed under evacuation orders amid the latest outbreak of war between Israel and Gaza's militant rulers, Hamas.

Meanwhile, the International Rescue Committee warned Wednesday that more military operations in Rafah would "significantly disrupt aid transfers from Egypt and prevent aid agencies from delivering even the most basic services to the Palestinian people who were told by Israel they would be safe there."

"More than half of Gaza's 2.2 million population are seeking refuge in Rafah, with the majority residing in temporary shelters, tents, or exposed to the elements," Bob Kitchen, vice resident of emergencies at the IRC, said in a statement. "Within the last 48 hours, airstrikes on residential zones in Rafah have killed at least 11 Palestinians, two of them children. If Israel expands its operations further south, it would mean the renewed forced displacement of more than a million people who have nowhere left to go; and it would end the humanitarian lifeline from Egypt."

"If they aren't killed in the fighting, Palestinian children, women and men will be at risk of dying by starvation or disease," Kitchen added. "There will no longer be a single 'safe' area for Palestinians to go to as their homes, markets, and health services have been annihilated."

Both the IRC and the Norwegian Refugee Council are calling for the warring sides to agree to an immediate cease-fire.

-ABC News' Zoe Magee and Morgan Winsor

Secretary of State Antony Blinken said he believes a hostage deal is still within reach, despite Israeli Prime Minister Benjamin Netanyahu’s earlier comments rejecting Hamas’ counteroffer.

"We had an opportunity to discuss with the Israeli government the response that Hamas sent last night to the proposal that the United States, Qatar and Egypt have put together to bring the remaining hostages and extend the humanitarian pause," Blinken said at a news conference in Israel Wednesday. "What I can tell you about these discussions is that while there are some clear nonstarters in Hamas' response, we do think it creates space for agreement to be reached and we will work at that relentlessly until we get there."

Blinken later added, "These things are always negotiations. It's not flipping a light switch."

Blinken said he plans to meet with the families of hostages on Thursday.

As for Israel’s growing offensive in Gaza, Blinken stressed that "any military operation that Israel undertakes needs to put civilians first and foremost in mind."

Blinken said he had outlined specific measures the U.S. expected to see during his "extensive" talks with Netanyahu and Israeli national security leaders.

He said Israel should open a border crossing between Israel and northern Gaza to help improve the flow of humanitarian aid.

-ABC News' Shannon Crawford

Freed Israeli hostages and families of those still being held hostage by Hamas are speaking out, pleading for Israeli Prime Minister Benjamin Netanyahu to agree to a hostage deal, after the prime minister on Wednesday rejected the current proposed deal.

Netanyahu called the deal "delusional," and described it as a "surrender" that would lead to another massacre.

Adina Moshe, who was released after being held hostage for 49 days, said Wednesday, "We love our country. ... But I want my country back and its morality that is gone."

"I fear for the lives and fates of the hostages," Moshe said. "I'm afraid we'll have nothing to pass on to our grandchildren and great-grandchildren. Please, prime minister: If you continue on this path, there will be no more hostages to release. Restore our trust -- release them now."

Sahar Calderon, a 16-year-old who was released after being held hostage for 54 days, said, "Every hour there was hell. . … A terrorist glared at me for 24 hours with murder in his eyes, and every minute I feared being raped."

Calderon’s father is still being held hostage.

"I am grateful to the government for bringing me back, but what about my father, who is abandoned anew every day, uncertain if he will live or die?" she said. "Bring him back -- do not make me lose faith in our country a second time."

Israeli Prime Minister Benjamin Netanyahu is defending the Israeli military’s continued bombardment of Gaza, targeting Hamas fighters, after President Joe Biden criticized the campaign as "over the top" given the dire conditions and high death toll in the Palestinian territory.

When asked about Biden's remark in a Sunday interview with ABC News' "This Week" co-anchor Jonathan Karl, Netanyahu said he appreciated the president's support thus far and laid the blame for civilian casualties on the Hamas terrorist group, which launched an unprecedented surprise attack on Israel on Oct. 7.

"I don't know exactly what he [Biden] meant by that, but put yourself in Israel's shoes. We were attacked. Unprovoked attack, murderous attack on Oct. 7," Netanyahu said, adding, "I think we've responded in a way that goes after the terrorists and tries to minimize the civilian population in which the terrorists embed themselves and use them as human shields." The Israel Defense Forces has said it is only targeting Hamas and other militants in Gaza and alleges that Hamas deliberately shelters behind civilians, which the group denies.

Karl pressed Netanyahu on the number of deaths, with the Hamas-run Gaza Ministry of Health estimating more than 28,000 killed. Netanyahu acknowledged many civilians had been killed but claimed -- without presenting evidence -- that Israel's military is currently killing more Hamas fighters than civilians.

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-ABC News' Tal Axelrod