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

A mother of four in Gaza told ABC News she is worried about getting vaccinations for her days-old newborn and keeping her children warm and fed.

"I'm afraid for him because there is no warmth, no vaccinations, and no good health supplies," Maha al Sharbsy, 32, said of her fourth child, Mohammed, who was born on Saturday. "The child has started to show signs of jaundice, and his condition is unstable."

Al Sharbsy said she and her children evacuated northern Gaza days after the war started following "intense" bombings. Now in southern Gaza, she said her children cannot sleep "because there are no winter clothes and no food," and she doesn't have money to buy food.

"I want the children to live in peace, cleanliness, and good health conditions. At the very least, for the sake of the children," she said. "We, the adults, are not the issue; the children are what matter."

Her 9-year-old son, Riad, told ABC News he misses his room and toys and is worried for his family.

"I'm afraid of the rockets, I'm afraid of people getting injured and dying, and I'm afraid of planes bombing our homes," he said.

-ABC News' Sami Zayara and Zoe Magee

One month into the Israel-Hamas war, the International Committee of the Red Cross called on both sides to "deescalate now" to prevent more suffering among the civilians in Gaza and Israel, particularly children.

The organization called for the release of hostages "immediately" and for the restoration of "critical services," such as water, electricity and health care, in Gaza.

"Among the most shocking impact is the agony children have had to bear. Children have been ripped from their families and held hostage. In Gaza, ICRC surgeons treat toddlers whose skin is charred from widespread burns," ICRC President Mirjana Spoljaric said in a statement. "What more must children endure? The images of suffering, dead and wounded children will haunt us all. This is a moral failing."

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