(CNN) -- Authorities arrested the father of three missing Michigan boys Tuesday, charging him with parental kidnapping, officials said.
John Skelton was arrested immediately upon his release from a mental health facility where he was being treated after an attempted suicide, Morenci, Michigan, Police Chief Larry Weeks told reporters.
Weeks said investigators have not found the children, despite internet rumors that began circulating Tuesday of their whereabouts.
Local authorities and federal investigators have been trying to find the children since Friday. But Tuesday morning, Weeks said investigators "do not anticipate a positive outcome."
Investigators are skeptical of information Skelton has provided them, he said.
Skelton said he left the three boys with a woman, whom he identified as Joann Taylor, the morning before he tried to take his own life -- in part to ensure they did not witness his suicide attempt.
Skelton said Taylor was supposed to take the boys to their home in Morenci, a southern Michigan town of about 2,400 people about 40 miles west-northwest of Toledo, Ohio, Friday afternoon, Weeks said.
But the boys -- Tanner Skelton, 5, Alexander William Skelton, 7, and Andrew Skelton, 9 -- never arrived.
Earlier, authorities determined that Skelton had no "established relationship" with the person he named as Taylor, and they aren't certain that she even exists.
Authorities continue to ask for the public's help, hoping that someone saw Skelton's blue 2000 Dodge Caravan, in which he was believed to be carrying the boys from 2:30 p.m. Thursday to 1:30 p.m. Friday somewhere along a 25-mile stretch of road between Morenci and Holiday City, Ohio.
Weeks had been more optimistic Monday, saying, "We remain hopeful. "That's why we're doing what we're doing, and hope to bring these boys home."
The last time a non-family member saw the boys was at 5 p.m. on Thursday, according to the chief.
Police say Tanner is 3 feet, 6 inches tall with strawberry blond hair and blue eyes, and weighs about 40 pounds. Alexander is 3 feet, 9 inches tall, has brown hair and eyes, weighs about 45 pounds and has scars on his hairline and chin. The oldest brother, Andrew, is 4 feet, 1 inch tall, has brown hair and eyes and weighs roughly 57 pounds.
Andy Arena, a special agent with the FBI, also has called for help from the public. "We need calls. We need tips. Anything that's out there, no matter how incredible you may think it is, call. Let us know," he said Sunday.