President Joe Biden told ABC News' Karen Travers that he asked Israeli Prime Minister Benjamin Netanyahu "for a pause" in fighting during a phone call Monday.

"I didn't get a chance to talk to him today, but I did ask him for a pause…yesterday," Biden said.

When asked for a specific timeline of the pause, the president did not answer.

-ABC News' Justin Fishel and Karen Travers

Israeli Prime Minister Benjamin Netanyahu said Tuesday that Israel Defense Forces have "encircled" Gaza City and are "operating inside it."

"We are increasing pressure on Hamas every hour, every day," he said in remarks translated by Reuters. "We have killed thousands of terrorists, above ground and below ground."

Maj. Gen. Yaron Finkelman, the commander of IDF's Southern Command, said Tuesday they are fighting in "significant centers of the Gaza Strip."

"For the first time in a decade, the IDF is fighting in the heart of Gaza City," Finkelman said in a statement. "Today, at this very hour, our soldiers are eliminating terrorists, discovering tunnels, destroying weapons and continuing to advance into the center of the enemy."

Dr. Ghassan Abu Sitta, a British-Palestinian plastic surgeon, called the conditions of working in a hospital in Gaza right now "medieval."

"There's no pain relief," he told ABC News in a phone interview on Tuesday. "I mean, we operate on patients and then we give them all paracetamol. We've run out of morphine two weeks ago."

Abu Sitta, who has been working at the Shifa and Ahli hospitals in Gaza, said they have had to perform surgery on some children without proper anesthesia.

"These kids are traumatized," he said.

He has seen children who come in with no surviving family, he said.

"It really is heart-wrenching," he said. "From the minute you see them in the emergency room with no one around them, you realize."

-ABC News' Zoe Magee

Israeli Prime Minister Benjamin Netanyahu doubled down on his position in brief remarks Tuesday, saying "there will be no cease-fire without the return of the hostages."

Netanyahu also said he has asked the International Committee of the Red Cross to visit the hostages and report on their well-being.

The prime minister offered a warning to both Hamas and Hezbollah, saying in Hebrew remarks, "Gaza will never be a threat to Israel again," and adding, "If Hezbollah chooses to join the war, it will make the mistake of its life."

Netanyahu said he speaks with President Joe Biden frequently and that he "deeply appreciates" his support, as well as the support of the US Congress and American people.

-ABC News' Jordana Miller

During brief remarks in New Delhi Friday morning, U.S. Secretary of State Antony Blinken swiftly acknowledged the Biden administration’s “appreciation” of Israel’s commitment to four-hour pauses with three-hour notice in specific areas and corridors of Gaza “that will allow people to move more safely, freely to get out of harm's way and also to access assistance.”

“At the same time, much more needs to be done to protect civilians and to make sure that humanitarian assistance reaches them," he continued. "Far too many Palestinians have been killed. Far too many have suffered these past weeks, and we want to do everything possible to prevent harm to them, and to maximize the assistance that gets to them.”

The secretary said they have established basic principles to guide the effort for lasting peace and security in the region: no use of Gaza as a platform for launching attacks against Israel, no diminution in the territory of Gaza and a commitment to Palestinian-led governance.

Blinken reaffirmed that the administration had “long been committed” to a two-state solution, and the terror attacks of Oct. 7, he said, only redouble American commitment to the peace process.

“But now we've had the events of October 7 -- the almost, beyond the human imagination -- horror of October 7. And I think that only reinforces us in our conviction and our commitment to durable and lasting peace which again, we see through two states,” he said.

On humanitarian assistance, Blinken said that “more than plans, we have a concrete way forward,” including ensuring that there are adequate supplies of fuel for the trucks coming in and that hospitals and desalination plants “have what they need.”

“It's always a process and moving from an understanding, moving from an agreement to implementation is what we're working on right now,” he said.