International Committee for the Red Cross Director-General Robert Mardini said the Red Cross "offered our role of neutral intermediary to facilitate any negotiated release of hostages," and that "offer still stands."

"We hope that the parties will reach more agreements to free hostages on one side and Palestine detainees on the other," Mardini said.

As the fighting between Israel and Hamas resumes, he stressed that hospitals should be spared.

"It is very unfortunate what we were seeing over the past weeks -- hospitals becoming battlegrounds, fighting happening inside and around hospitals. And this is why we keep and we will keep on repeating … that hospitals should be preserved," he said.

When Hamas militants opened fire at a Jerusalem bus stop Thursday morning, Hamas killed three of the victims, and an Israeli Defense Forces soldier at the scene mistakenly shot and killed the fourth victim, the IDF said.

The deadly incident unfolded around 7:40 a.m. local time when a pair of heavily armed assailants drove up to the bus stop, got out of their vehicle and opened fire on civilians, killing three and injuring others. Both gunmen were killed by two off-duty Israeli soldiers and armed Israeli civilian Yuval Doron Castleman who were near the scene, according to Israeli police.

Israeli police identified the two suspects as brothers in their 30s from the Sur Baker neighborhood of East Jerusalem. Both Israeli police and Israeli Prime Minister Benjamin Netanyahu described the gunmen as "terrorists."

Hamas claimed responsibility for the deadly shooting, saying in a statement that the attack was in response to Israel's "unprecedented crimes" including "brutal massacres" in Gaza and the killing of children in the occupied West Bank.

The IDF said Friday that, during the attack, one of the IDF soldiers at the scene "mistakenly suspected" that Castleman, the armed Israeli civilian "who acted bravely and courageously to neutralize the terrorists," was a third terrorist.

"The same soldier also fired at him which led to his serious injury and tragic death," the IDF said.

The investigation of the attack continues," the IDF said. "We share in the grief of the family members of the late Yuval who acted bravely and saved lives, and in the grief of other families murdered in the attack and wish for the speedy recovery of the injured."

As Secretary of State Antony Blinken left Israel on Friday, he was asked about a report by The New York Times alleging Israel knew about Hamas' attack plan a year in advance.

"There's going to be plenty of opportunity for a full accounting of … looking back to see what happened [and] who knew what, when -- Israel has been very clear about that," Blinken said.

"Right now, the focus is on making sure that [Israel] can do everything possible to ensure that it doesn't happen again, make sure that civilians are protected, and that humanitarian assistance gets in, and as I said, to also look at what happens once this conflict is over -- what happens in Gaza, what happens more broadly getting us on a path to lasting security," Blinken continued. "So we're focused on on all of that. I think there'll be time, and I know this will happen -- there will be accountability, looking at what led up to Oct. 7."

-ABC News' Nate Luna

As fighting between Israel and Hamas resumes, Israel's "relentless bombardment" in Gaza on Friday has been "utterly terrifying" -- and has had an immediate impact “on the faces of children," UNICEF spokesperson James Elder told ABC News.

"I feel I was starting to see childhood return when you chat to them -- that’s been replaced by fear again," Elder said. "There’s a trauma which returns very quickly."

Elder described seeing "children lying on the floor with limbs missing." He said some children who had already been injured were being moved around hospitals to make room for other casualties to come in.

He said sanitation "has broken down" and Gaza’s hospitals are now "on life support."

“Disease threatens just as many children" as the bombings, he said.

Over the last seven days, aid has been reaching Gaza, he said, but, "seven days was never ever enough.”

Elder said he’s "terrified" that if the fighting continues for even another couple of weeks, “many, many more thousands of people" could be killed.

-ABC News' Tom Soufi Burridge, Zoe Magee, Angus Hines and Nicky De Blois

The United Nations said 138,000 liters of fuel entered Gaza on Saturday -- the highest amount in one day since the Israel-Hamas war began.

Trucks with food, water, medicine and medical supplies also entered Gaza on Saturday, according to the U.N. Office for the Coordination of Humanitarian Affairs.