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."

During brief remarks in New Delhi Friday morning, U.S. Secretary of State Antony Blinken swiftly acknowledged the Biden administration’s “appreciation” of Israel’s commitment to four-hour pauses with three-hour notice in specific areas and corridors of Gaza “that will allow people to move more safely, freely to get out of harm's way and also to access assistance.”

“At the same time, much more needs to be done to protect civilians and to make sure that humanitarian assistance reaches them," he continued. "Far too many Palestinians have been killed. Far too many have suffered these past weeks, and we want to do everything possible to prevent harm to them, and to maximize the assistance that gets to them.”

The secretary said they have established basic principles to guide the effort for lasting peace and security in the region: no use of Gaza as a platform for launching attacks against Israel, no diminution in the territory of Gaza and a commitment to Palestinian-led governance.

Blinken reaffirmed that the administration had “long been committed” to a two-state solution, and the terror attacks of Oct. 7, he said, only redouble American commitment to the peace process.

“But now we've had the events of October 7 -- the almost, beyond the human imagination -- horror of October 7. And I think that only reinforces us in our conviction and our commitment to durable and lasting peace which again, we see through two states,” he said.

On humanitarian assistance, Blinken said that “more than plans, we have a concrete way forward,” including ensuring that there are adequate supplies of fuel for the trucks coming in and that hospitals and desalination plants “have what they need.”

“It's always a process and moving from an understanding, moving from an agreement to implementation is what we're working on right now,” he said.