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

Secretary of State Antony Blinken traveled to Iraq to meet with Iraqi Prime Minister Mohammed Shia al-Sudani on Sunday following the secretary's visits to Israel, Jordan and the West Bank.

Blinken told reporters that his meeting with the Iraqi prime minister was productive and said he emphasized the need to prevent spillover from the conflict in Gaza.

"I made very clear that the attacks, the threats coming from militia that are aligned with Iran are totally unacceptable," Blinken said. "We're not looking for conflict with Iran. We've made that very clear. But we'll do what's necessary to protect our personnel."

"We're working very hard to make sure that the conflict in Gaza does not escalate, does not spread to other places, whether it's here, whether it's elsewhere in the region," he said.

Blinken was asked about Arab leaders' instance that nothing short of a total cease-fire would be acceptable.

"I think everyone would welcome humanitarian pauses -- there's no doubt about that," Blinken responded.

He said pauses "advance things that we're all trying to accomplish," including getting more humanitarian aid into Gaza, getting people out of Gaza and getting hostages home.

On his meeting with Palestinian Authority President Mahmoud Abbas, Blinken said the PA was "playing a very important role right now in the West Bank in trying to keep stability there."

-ABC News' Shannon Crawford