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

President Joe Biden and Israeli Prime Minister Benjamin Netanyahu discussed Monday the possibility of "tactical pauses" in strikes on Gaza to help civilians reach safer locations, allow for more humanitarian aid to get in and help work toward the possibility of hostages being released, according to the White House.

"We consider ourselves at the beginning of this conversation, not at the end of it, so you can expect that we're going to continue to advocate for temporary vocalized pauses in the fighting," National Security Council spokesman John Kirby said.

He said less than 30 trucks of humanitarian assistance arrived in Gaza over the past 24 hours, which he said wasn't enough.

“In the early goings here, Israel was very resistant to humanitarian assistance getting in at all, and we persisted. We continue to persist," Kirby said. "Humanitarian aid is getting in, again, not to the degree we want it to, I'm not going to sugarcoat it. But, but, my goodness, based on our constant engagement, we've been able to make a big difference."

Kirby said "more Americans" will be leaving Gaza on Monday but he did not provide specific numbers.

Kirby said Biden and Netanyahu also discussed the situation in the West Bank and "reducing threats from terrorist groups that are operating there."

Kirby said their talks would continue and the leaders agreed to speak "in the coming day."

-ABC News' Justin Ryan Gomez