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."

Through tears and voices choked with raw emotion, people whose family members are believed to held hostage by Hamas pleaded for help during a Republican-led press conference at the U.S. Capitol on Tuesday.

Doris Liber told reporters that her son, Guy Iluz, called her as Hamas unleashed its terrorist attack against Israel on Oct. 7 and she hasn't heard from him since.

"I'm here because it's been 30 days. Every day is like eternity to me," Liber, who holds joint Israeli-American citizenship, said. "We don't have a list of the hostages. We don't know their condition. I don't have anything. So I need your help."

She described the last time she spoke to her son.

"We hear shots in the background," she said. "He was shot in the arm and he wasn't able to stop the bleeding and he was trying to say his last words."

“I tried to, you know, tell him, ‘Guy I love you. Don't worry, nothing's going to happen. I'm going to end the call now. I'm going to send somebody now to get you,'" she continued. "And that's what I did. I hung up and I regret that since I didn't hear from him since."

Yonatan Lulu-Shamriz said he was awoken by his pregnant wife as the sirens began to sound in their kibbutz. They grabbed their 3-year-old daughter, huddled in a safe room and listened as their neighbors were slaughtered, he said. Soon his brother, Alon, called to report he was under attack, Lulu-Shamriz said.

“We don't know what is their condition," Lulu-Shamriz said. "This is a wake-up call not only for Israel, not only for the Jewish community. This is a wake-up call for all of you -- all of you here, all of America, all of Europe. You are next. You are next. And we should do everything that we can to stop these atrocities."

House Speaker Mike Johnson vowed to "take action."

"We're resolved to help," the newly minted speaker said. "House Republicans want to do that."

-ABC News' John Parkinson and Lauren Peller