The Israel Defense Forces is "deepening" its operational activities and putting pressure on Gaza City, IDF spokesman Daniel Hagari said in Hebrew.

Israeli forces have killed Hamas leaders who were part of the Oct. 7 attack on Israel and soldiers are destroying Hamas tunnels one-by-one, Hagari said.

In the West Bank, the IDF said it killed four armed terrorists who were allegedly involved in attacks on Israel.

To the north, in Lebanon, the IDF is in the middle of extensive attacks in response to 30 rockets allegedly fired at Israel on Monday, Hagari said.

-ABC News' Jordana Miller

More than 300 U.S. citizens and lawful permanent residents have left Gaza since the start of November, and that number's expected to rise, State Department spokesman Vedant Patel said.

After the Rafah border crossing between Egypt and Gaza closed over the weekend, Patel said the State Department understood it reopened on Monday.

Asked about the apparent contrast between Secretary of State Antony Blinken’s assessment that all parties were "working through" practical issues surrounding humanitarian pauses and Israeli Prime Minister Benjamin Netanyahu’s insistence that there will be no pauses until Hamas releases hostages imprisoned in Gaza, Patel said, "I don't think that these circumstances in these situations are black and white, necessarily."

“We will continue to raise publicly, privately, directly with our Israeli partners what we believe to be avenues to allow for humanitarian aid to get into Gaza to support the Palestinian civilians who need it. And of course, Israel will continue to conduct and make assessments about this operation, as they're the ones doing so," he said.

-ABC News' Shannon Crawford

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

Eighty-eight workers with UNRWA, the United Nations agency for Palestinian refugees, have been killed since Oct. 7, the highest number ever seen in a single conflict, the agency said.

A UNRWA spokesperson said the 88 fatalities are "only what we could verify -- the actual number could be even higher."

"Like most Gazans, our staff have also lost relatives, friends, neighbors and are themselves displaced with their families," UNRWA said. "And yet, they continue to work tirelessly to provide humanitarian assistance."

At least three premature babies have died at the Al-Shifa Hospital in the Gaza Strip when a missile struck nearby and shut down the medical facility's backup generator, according to a doctor working at the hospital.

Dr. Ahmed Mokhallalti, the chief plastic surgeon at the hospital, told ABC News that the babies died when the power to their incubators was cut off Friday night into Saturday morning.

Mokhallalti said all of the hospital's ventilators were back up and running Sunday, but he expressed fear that more people would die at the hospital due to the relentless bombing.

Hospital officials said two patients in the hospital's intensive care unit also died on Sunday due to complications caused by the shelling.

The international humanitarian group Doctors Without Borders has made repeated calls for the shelling of hospitals in Gaza to cease.

"We are nearly sure that we are alone now. No one hears us," Dr. Mohammed Obeid of Doctors Without Borders said in a video statement from the Al-Shifa Hospital on Saturday.

Obeid said there are about 600 patients at the hospital who need medical care and need to be evacuated.

"The problem is [we need] to be sure we can evacuate the neonatal patients because we have 37 to 40 premature babies," Obeid said. "We have about 17 other patients in the ICU, and we have 600 postoperative patients who need medical care. So the situation is very bad. We need help."

-ABC News' Zoe Magee, Matt Gutman and Sami Zayara