(CNN) -- A man has admitted he killed his uncle's 6-year-old stepdaughter, whose body was found in a Louisiana trash can this week, a spokesman for the Jefferson Parish Sheriff's Office said Wednesday.
Matthew Flugence admitted to detectives Wednesday morning that he stabbed Ahlittia North, a girl he previously babysat, over the weekend, Col. John Fortunato said.
Flugence, 20, was arrested in the case on Tuesday, the day authorities found Ahlittia's body in a trash can down the street from her mother and stepfather's apartment in the New Orleans suburb of Harvey.
Flugence, who had an outstanding warrant charging him with sexually assaulting an 11-year-old girl last year, has been charged with murder in Ahlittia's death, Fortunato said.
"I don't know what I else I can say about the character of an individual that just admitted to killing a 6-year-old," Sheriff Newell Normand told reporters Wednesday morning when asked about Flugence's background. "I think that speaks for itself."
Flugence's brother Russell, 21, was arrested on suspicion of obstructing justice in Ahlittia's death, Normand said earlier this week. Russell Flugence had information about the crime that he didn't come forward with, and he also had information implicating his brother, the sheriff asserted.
Matthew Flugence told investigators that he killed Ahlittia after finding her early Saturday outside the Harvey apartment where her mother and her stepfather -- Flugence's uncle -- lived, Normand said Wednesday.
"(Flugence's) story is (that) in the early morning hours ... he happened to see her out and about, and he was out and about, walking through the neighborhood," Normand said.
The investigation began after Ahlittia's mother awoke Saturday to find her gone from the apartment, authorities said. The girl was living with her mother for the summer, but normally lived with someone else in Donaldsonville, about 60 miles to the west, Normand said.
After she was reported missing, investigators spent Saturday combing the neighborhood, looking in alleys, Dumpsters and boarded-up fourplexes. They found a pool of blood in one of the buildings, Normand said, and when DNA results came back Monday evening showing the blood belonged to Ahlittia, investigators searched the area again.
That's when they found the girl's body in a garbage can, wrapped in a blanket from her house and covered in a garbage bag, Normand said.
Investigators looked at the garbage can during their first search of the neighborhood, so they know the body was put inside sometime after Saturday, he said.
Flugence told detectives Wednesday that he killed Ahlittia on Saturday with a knife that investigators found on him when he was arrested, Normand said.
Flugence was arrested Tuesday after people told authorities that he was walking along a road in nearby Westwego, asking for money and telling them he was on the run from police, officials said.
Ahlittia suffered four stab wounds -- two to her neck, likely the fatal wounds, and two to the abdomen, Jefferson Parish Coroner Gerald Cvitanovich said. She also had bruises to the front and back of her head, shoulder, lower back, and lower extremities.
Cvitanovich said were no obvious signs during an autopsy of sexual assault.
When asked Wednesday whether it was hard to believe that Flugence's relatives didn't know about the sexual assault warrant, Normand said: "No."
"A lot of that information came about during the course of this investigation" into Ahlittia's death, he said.
CNN's Melissa Gray and Dave Alsup contributed to this report.