Qatar and Egypt have received a response from Hamas and the Palestinian factions regarding the truce proposal, the Qatari Foreign Ministry said Tuesday.

Hamas and Islamic Jihad said in a statement, "The response prioritizes the interest of our Palestinian people. The need to completely stop the ongoing aggression against Gaza. The Palestinian delegation expressed its readiness to deal positively to reach an agreement to end this war against our people, based on a sense of national responsibility."

A U.S. official familiar with negotiations describes Hamas’ response as not an outright yes or no, but a counter with questions about provisions included in the proposal and some additional demands.

Another official said that while the U.S. is still analyzing Hamas’ response, mediators see the potential to bridge remaining gaps at this point and will coordinate with all parties involved on the next steps -- which will likely include another round of talks.

Israel received the Hamas response from the mediators Tuesday evening, according to a senior Israeli official. In its response, Hamas rejected the outline of the deal for the release of the abductees presented by President Joe Biden, the official said.

-ABC News' Shannon Crawford and Dana Savir

All four hostages rescued from Gaza this weekend have been discharged from hospitals, local officials told ABC News.

The three male hostages -- Almog Meir Jan, 22; Andrei Kozlov,27; and Shlomi Ziv, 41 -- were discharged from Sheba Medical Center on Tuesday, according to the medical center.

Noa Argamani, 26, was transferred to Ichilov Medical Center on Saturday to be with her mother, who is in the hospital, officials said. Argamani was discharged on Tuesday morning, a hospital spokeswoman told ABC News.

-ABC News Jordana Miller and Dana Savir

The U.S. announced $404 million in aid for Palestinian civilians in Gaza and the region, bringing the total amount of aid from the U.S. to over $674 million since the wore broke out, the State Department announced Tuesday.

"This new funding will provide essential support to vulnerable Palestinians in Gaza, the West Bank and the region, including food, safe drinking water, health care, protection, education, shelter, and psychosocial support," the State Department said. "We urge other donors to contribute to the humanitarian response in Gaza and the region, increase support to those affected by the conflict, and work together to find lasting solutions to the crisis."

United Nation human rights officials said they were "profoundly shocked" by the Israeli operation that freed four hostages in central Gaza over the weekend, adding that actions by both Israel and Hamas "may amount to war crimes."

"The manner in which the raid was conducted in such a densely populated area seriously calls into question whether the principles of distinction, proportionality and precaution -- as set out under the laws of war -- were respected by the Israeli forces," the U.N. Office of the High Commissioner of Human Rights, or OHCHR, said in a statement on Tuesday.

The rescue operation in a refugee camp in Nuseirat killed as many as 274 people, the Hamas-run Gaza Health Ministry said Monday. Hundreds of others were injured, the ministry said. Many of those injured and killed were Palestinian civilians, OHCHR said on Tuesday.

But OHCHR also said it was "deeply distressed" about the way the militant groups continue to hold hostages, "most of them civilians, which is prohibited by international law."

By holding those hostages in densely populated areas, Hamas militants are putting civilians and the hostages at risk, the agency said.

"All these actions, by both parties, may amount to war crimes," OHCHR said.

-ABC News' Joe Simonetti and Kevin Shalvey

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