An 11-year-old California girl snatched from the street in front of her house in 1991 had two children with the man accused of taking her and was forced along with the children to live in backyard sheds, police said Thursday. 

"From what they have both said, he fathered both of those children with Jaycee [Dugard]," El Dorado County Undersheriff Fred Kollar told reporters.

The girls, now 11 and 15, had been living with their mother, now 29, in a series of sheds behind Garrido's house in Antioch, California, until they were discovered on Wednesday, Kollar said.

"None of the children had ever gone to school, they had never been to a doctor, they were kept in complete isolation in this compound, if you will, at the rear of the house," he said. "They were born there."

In a rambling telephone interview from jail, Garrido told CNN affiliate KCRA of Sacramento he was relieved at being caught.

"I feel much better now," he said. "This is a process that needed to take place."

Kollar said Garrido's wife, Nancy, was with her husband when Dugard was abducted from the street in front of her house in South Lake Tahoe. Garrido was already a registered sex offender at the time.

"There was nothing then nor is there anything now to indicate that this was anything other than a stranger abduction of an 11-year-old," Kollar said.

The investigation went years without apparent progress until Tuesday, when Garrido showed up on the campus of the University of California at Berkeley with his two daughters and attempted to get permission to hand out literature and speak, Kollar said. He did not know the subject of either the literature or the planned talk.

Police officers "thought the interaction between the older male and the two young females was rather suspicious," so she confronted them and performed a background check on him, Kollar said.

That check revealed that Garrido was on federal parole for a 1971 conviction for rape and kidnapping, for which he had served time in the federal penitentiary at Leavenworth, Kansas.

A school spokesman identified the officers as Allison Jacobs and Lisa Campbell, and said the two became suspicious of "subtle behavior" Garrido exhibited.

They passed on the information to Garrido's parole officer, who requested that the 58-year-old man appear Wednesday at the parole office.

Garrido did just that, accompanied by his wife, Nancy, "and a female named Allissa," Kollar said.

The presence of "Allissa" and the two children surprised the parole officer, who had never seen them during visits to Garrido's house, Kollar said.

"Ultimately, Allissa was identified as Dugard," Kollar said.

DNA confirmation is being sought to confirm her identity, but Dugard revealed information during an interview that only she could have known, Kollar said.

"The two minor children turned out to be children of Jaycee and the male suspect, Garrido," he said.

Scott Kernan, undersecretary of the California Department of Corrections and Rehabilitation, told reporters that Garrido admitted to having abducted Dugard.

El Dorado County Sheriff's Office online records showed that Phillip and Nancy Garrido were in the county jail, held on suspicion of offenses including conspiracy to commit a crime and kidnapping with the intent to commit robbery and rape.

Dugard had been living behind Garrido's home since she was kidnapped, Kollar said.

But her presence there apparently went unnoticed by others in the residential neighborhood, where homes on one-fourth to one-half-acre lots typically sell for less than $200,000, said Kathy Russo, whose father has lived two houses away from the Garridos for 33 years.

"My dad said he never saw a young woman," said Russo, who added that her father, 94-year-old Dante Confetti, considered Garrido to be a "kind of strange, reclusive, kind of an angry kind of guy."

She said the one-story house's backyard was obscured by trees and ringed by a wooden fence.

Her family's last contact with Garrido was last fall, she said. "He was burning something in the backyard and my home health aide called the fire department," Russo said.

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