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

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