In a ruling on Wednesday, Winona County District Judge Mary Leahy said, "It is in the best interest of the children to remain in the protective care of the responsible social services agency," rather than being handed over to their father, Adam Fravel.
The video featured is from a previous report.
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Fravel did not have custodial rights to the children, ages 5 and 2, prior to the disappearance of their mother, Madeline Kingsbury, additional court documents show.
Adam Fravel denied any involvement in Kingsbury's disappearance in a statement Wednesday.
"Over the course of the last 12 days my family and I have been subject to a myriad of accusations regarding the disappearance of the mother of my children, Maddi Kingsbury. During these last 12 days I have cooperated with law enforcement at every turn, including sitting down for multiple interviews with Winona County law enforcement.
"I did not have anything to do with Maddi's disappearance. I want the mother of my 5-year-old and 2-year-old to be found and brought home safely. I want that more than anything," said Fravel.
Fravel said he had been advised by law enforcement on April 2 not to attend news conferences or assist in searches for Kingsbury due to safety concerns.
"My non-attendance and silence has been inferred by many as a sign of apathy, or worse. That could not be further from the truth. I want Maddi home and for her to be able to be with our two children," said Fravel.
Bonney Bowman, a spokesperson for the Minnesota Bureau of Criminal Apprehension, told CNN on Thursday she is not aware of any law enforcement agencies advising Fravel not to attend news conferences or organized searches for Kingsbury.
Asked whether Fravel has cooperated with law enforcement, Bowman said, "I'm not able to share that information at this time."
Kingsbury was last seen on the morning of March 31.
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She did not show up at work as expected the day she disappeared, and did not answer calls from family and friends, police said. She didn't pick up her children from day care that afternoon or make other arrangements.
The Winona County Health and Human Services Department was notified by police on April 4 that the two children "are in need of protection or services" after their mother was designated an endangered missing person, according to court documents obtained and reviewed by CNN.
The agency took custody of the children, who had been with their father at their grandparent's residence, according to court documents obtained by CNN.
Fravel doesn't have custodial rights to his children, but he had his children at his home and his parent's home, according to the documents.
When social workers confronted Fravel at the home last week, he was not cooperative with officials and initially did not allow them access to his children before he eventually placed them in HHS custody, the court documents say.
Evidence suggests Kingsbury's disappearance was "involuntary and suspicious," the Winona Police Department said in a Wednesday update.
"We remain extremely concerned for her safety," police said in their update.
"We have drafted and served numerous search warrants as part of our search efforts."
Kingsbury's family said in a statement Wednesday they have been working with investigators in the search for her. "Members of our family and close friends coordinate closely with law enforcement and send out search teams day after day, every day," the statement said.
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"We will find Madeline. This is our mission and we will not falter."
Police have said they believe her vehicle, a 2014 dark blue Chrysler Town and Country, may have traveled from Winona to eastern Fillmore County on the day of her disappearance.
They have asked residents in that area to check their "video cameras, doorbell cameras, game cameras ... for any signs of the van passing through or stopping."
A court appearance is scheduled on May 15 for a pre-trial hearing over the children's custody.
The judge ruled visitation between Fravel and the children prior to the trial "shall be at the reasonable discretion of Winona County Health and Human Services."
CNN has contacted Fravel's attorney for comment.
Winona is in southeastern Minnesota, near the Wisconsin border.
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