Secretary of State Antony Blinken on Wednesday said Israel "cannot occupy" Gaza "not now, not after the war."

The top U.S. diplomat added that a transition period may be necessary when the bombings and shooting stop in Gaza.

"I think we've been very clear from day one that when it comes to post-conflict governance in Gaza, a few things are clear and necessary," Blinken said in Tokyo, where he's attending G7 meetings. "One, Gaza cannot continue to be run by Hamas. That simply invites a repetition of Oct. 7, and Gaza used as a place from which to launch terrorist attacks. It's also clear that Israel cannot occupy Gaza."

Blinken said G7 members stood united on the globe's major crises. The group's "first focus was the crisis in the Middle East." The group's joint communique called for "humanitarian pauses," short of a cease-fire.

"We all agreed that humanitarian pauses would advance key objectives to protect Palestinian civilians, to increase the sustained flow of humanitarian assistance, to allow our citizens and foreign nationals to exit, and to facilitate the release of hostages," Blinken said

-ABC News' Christopher Boccia and Joe Simonetti

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

The Israeli military on Monday accused Hamas militants of building "a whole tunnel system under" Sheikh Hamad Hospital in Gaza.

The practice of using hospitals as civilian shields has been "absolutely normal" for the militants, IDF spokesperson Jonathan Conricus said.

"Why it is this important? Because hospitals and other humanitarian facilities are supposed to enjoy special protections," Conricus said in a morning briefing. "But what Hamas is doing is that they've violating that special protection and using it for combat purposes."

More than 500 people have died in at least 102 strikes near or on health care facilities since Oct. 7, the World Health Organization said on Sunday.

"Over half of health attacks and over a half of hospitals damaged were in Gaza City," WHO officials said on social media. "Health care is #NotATarget."

During Monday's briefing, Conricus shared an IDF video that he said demonstrated there were Hamas tunnels under the hospital. He also shared several photos that he said dated back to at least 2010, when the hospital was being constructed. The groundwork for the Hamas tunnels was put in place at that time, he said. ABC News was not immediately able to verify the claims.

In a photo said to be from 2023, rocket-launching sites could be seen along the outskirts of the facility, Conricus said. He presented another photo of what he said was the opening of a Hamas tunnel on the grounds.

"We know that underneath this entire complex, there's an entire Hamas infrastructure underground," Conricus said. "And it is absolutely normal. This is how Hamas operates all around the Gaza Strip."

-ABC News' Kevin Shalvey