The three children allegedly abducted by their father and taken out of the country were found this week in Honduras and are now back in the United States, family members told FOXNews.com on Friday.

U.S. officials are working on extraditing the father quickly — before he's released by Honduran authorities — so he can be brought back to the U.S. to face federal kidnapping charges.

Joel Hundley of Kansas City, Mo., took his children — Alexandria, 1, Elijah, 2, and Julianna, 4 — from the family's house in Kansas City, Mo., on Feb. 19, and flew with them to El Salvador, FBI officials said. He then took them to Honduras, where he was found Tuesday in a mountainous region of the country a few hours away from Tegucigalpa, the country's capital, Hundley's sister Shelley told FOXNews.com

"When we got the kids, they were dirty, just dirt on their faces, their hair … I saw them and the oldest …she almost looked like a homeless kid, just filthy and dirty," Shelley Hundley said. "But she just went right to me and hugged me ... it was just a happy, partial reunification there but what they wanted was Mommy."

The FBI led the hunt for the 34-year-old man — described by family members as "delusional" — who methodically planned and carried out a scheme to snatch his three young kids and smuggle them out of the country. Family members believe Hundley has been engaged in questionable sexual activities, and that they feared the children would become victims of a human trafficking or child prostitution ring.

Jeff Lanza, a spokesman for the FBI in Kansas City, confirmed to FOXNews.com that the children were back in the United States and were safe.

When the Hundley family got word that Joel was spotted in Honduras with the children, Shelley Hundley, along with Heather Hundley — Joel's wife — and another sister decided she would fly down while the American Embassy, Interpol and Honduras nailed down her brother's exact location.

"I just decided to go down and just be there," Shelley said. "I didn't really do much, I just headed down there and waited for the authorities to let me know what was going on."

She got the call around 1 a.m. Tuesday, saying that her brother and the children had been found in a car and were being held at a small police outpost. She said the children were malnourished, dehydrated, and the oldest, Julianna, who has a kidney malformation and urinary-tract problems, was in a lot of pain.

"I walked right up to him, I just could not say a word to him and he did not say a word to me. It was actually weird in that sense that they both were totally silent," Shelley Hundley said, describing the encounter with a brother she had feared would involve her nieces and nephews in deviant sexual activity and child prostitution.

While she would not elaborate on what was done to the children physically, Shelley said the children were receiving proper medical care back in the United States. Shelley, her sister and Heather are taking care of them.

"We'll just be helping out as a team," she said.

But the Hundley family's ordeal is far from over.

Shelley said a Honduran judge has said he will release Joel from prison there on Saturday if the U.S. cannot finish the extradition process by then. Joel is only being held by Honduran authorities on an immigration charge, Shelley said. She and her family are worried that Joel will do more damage to himself — and maybe to others — if he's not brought back to the U.S. to get help.

"Obviously we're really worried because it's a quick time frame for us to really get this all together and obviously a lot of it is political," Shelley said. "If he walks, he wouldn't be able to come back to the U.S. but he would be a danger, wherever he is."

Lanza of the FBI could not confirm the timetable set by the Honduran judge for Joel Hundley's release, but said the State Department is taking the lead in working on terms of his extradition and hopes to be able to pick him up "as soon as possible."

"Our goal is to get him picked up by the FBI to bring him back to this country to face federal charges in Missouri," Lanza said, adding that Hundley faces charges of international parental kidnapping once he's back in the United States.

"We're working to make it happen as soon as possible," he said.

Joel Hundley's scheme to abduct his own children culminated Feb. 19 when he told his wife, Heather, to go out and enjoy a day with friends or at a local spa. When she returned home later that day, she found the kids and Joel had vanished.

Shelley had said Joel has a history of reading sexually explicit material and participating in sexual chatrooms on the Internet. He also engaged in what she called "group sexual activity slime," even taking at least one child to a group activity on an occasion. He also had a history of violence toward his wife.