Algosensey|'This is against all rules': Israeli mom begs for return of 2 sons kidnapped by Hamas

Since her two sons,Algosensey ages 12 and 16, were abducted Saturday by Hamas militants who burst into their father's home, an Israeli mother says she has been unable to sleep or eat, haunted by the last words she heard before a phone call from her children was cut off -- her youngest boy, pleading with the gunman not to take him.

The mother, who spoke to ABC News' Linsey Davis, described the horrific moment her life was turned upside down and the agony and helplessness she has experienced since. She says she is holding onto hope that she will be reunited with her children but can't shake thoughts of them being held in some "dirty pit."

The woman, who asked not to be identified for security reasons, said her living nightmare began at 6:30 a.m. on Saturday when her children phoned her from their father's home on a kibbutz near the Gaza border when a red alert sounded in their agriculture community and hundreds of Hamas fighters stormed the border, entering southern Israel as rockets launched from Gaza filled the dawn sky.

She said she was at another nearby kibbutz with her spouse when the alarms sounded. Her sons, she said, immediately went into a safe room at their father's house and called her.

"I was on the phone to them every few minutes. Somewhere around half past 8:00 [a.m.], they started saying that they were hearing gunshots outside the house. I tried to calm them down, telling them it's probably the army or our people shooting," she said.

Israeli officials said that after Saturday's surprise attack, Hamas militants, many on motorcycles and in other vehicles, went from town to town randomly shooting Israeli citizens and taking others captive, carrying them back across the border into Gaza.

Shortly after trying to alleviate her children's fears, the mother told ABC News she started to receive text messages from her neighbors that sent panic through her body.

"Then texts were coming in from other members of the community, saying that terrorists are walking around trying to break into houses, trying to get in," she said.

She said her children phoned her again, "whispering that they think they heard someone breaking into the house."

"It took another 10 minutes or so, and I could hear two or three people speaking in Arabic outside the door getting in," the mother said. "My youngest, who's only 12, [was] saying to them, 'Don't take me, I'm too young.' That was it. The line cut off. That was the last time I heard from them."

Breaking into tears, the mother said, "They were taken from their homes, from their beds, by barbarians. I can't really find another word for it."

She said she later learned from a video posted online by Hamas that her children's father was injured in the attack and that he and his girlfriend were also taken hostage.

"I'm only hoping that they're together now," she said.

The mother said the safe room her children were dragged from proved unsafe in the unprecedented door-to-door assault of the Hamas militants.

"The safe rooms were built against missile attacks or earthquakes," she said. "They weren't meant to be locked against terrorists going into the houses."

She said the terrorists ransacked homes and stole property, and burned houses with families still inside them.

In one of the hardest-hit kibbutzim -- Kfar Aza, near the Gaza border, where ABC News was allowed in on Tuesday -- entire Israeli families were slaughtered, and bodies of militants killed in the attack remained sprawled in the streets, some next to crashed motorcycles. Nearly every home in Kfar Aza was bullet-riddled, and a gaping hole in a nearby border fence remained open and guarded by Israeli soldiers still engaging in intense firefights with the enemy.

In remarks at the White House Tuesday, President Biden described "Hamas' bloodthirstiness" as reminiscent of ISIS rampages -- including "stomach churning reports of babies being killed."

"There are moments in this life, and I mean this literally, when pure, unadulterated evil is unleashed on this world," Biden said

"They took babies, they took women, they took children. They took elderly people over 85. They took people who were sick. They took injured people. They're just, you know, barbarians. I'm sorry, but I can't find another word for it," the mother told ABC News.

Her voice choking with emotion, she added, "I want the world to know that they're holding innocent civilians. I want the world to know that war has rules, even war has rules. Even ancient wars had rules. This is against all rules, against all rules of humanity, against all rules of war, against all rules of peace."

She said that while she has been in contact with officials from the Israeli government, they haven't given her any new information on the whereabouts of her sons.

Making matters even more harrowing is the statement from Hamas leaders on Monday, threatening to begin killing hostages one by one and filming the executions if their demands are not met.

"I want the world to demand the release of those innocent civilians. I want these children and women and babies back home, and I want my children back home," the mother said. "I can't take a shower without thinking of them being held hostage in some dirty pit somewhere. I can't eat, I can't sleep. I don't think human beings treat people like this. I'm sorry. I want the world to know, to demand those hostages to be returned to their homes."

She said she used to tell her children to be sympathetic to the Palestinian children, reminding them that the lives of kids in Gaza were much worse than theirs.

"I'm begging from a mother to other mothers in every country in the world to think what she would feel like if it was their child," she said. "Even mothers in Gaza want a normal life, I'm sure."