Brown cautioned late Sunday that his detectives were still working to confirm the sightings, backing away from earlier assurances that the witness accounts were genuine. But he was confident Laurean would soon be in custody.
"It will be a short trip - a short vacation - for Mr. Laurean," Brown said. "His vacation may be short, his travel may be long, but I hope we'll be there to help him return."
On Saturday, authorities said they recovered what they believe to be the burned remains of Marine Lance Cpl. Maria Lauterbach and her unborn child from a fire pit in Laurean's backyard, where they suspect he burned and buried her body.
Those remains have been sent to the state medical examiner's office in Chapel Hill for a formal identification.
That same day, state authorities issued an arrest warrant on murder charges for Laurean, 21, of the Las Vegas area. They believe he fled Jacksonville before dawn Friday after leaving behind a note in which he admitted burying her body but claimed Lauterbach cut her own throat in a suicide.
Brown has challenged Laurean's assertion that Lauterbach killed herself, citing what he described as evidence of a violent confrontation inside Laurean's home - blood spatters on the ceiling and a massive amount of blood on the wall.
Brown said Sunday that evidence in the case "leads us to believe that he would be a dangerous and violent person if put in a corner."
"What I've seen and what we've discovered indicates he does have a real heinous behavior about him," he said.
Brown has said Lauterbach purchased a bus ticket to El Paso, Texas, around the time of her disappearance, but said Sunday authorities are not in possession of the ticket. Shreveport is roughly 950 miles southwest of Jacksonville, and is about two dozen miles from the Texas state line and more than 800 miles east of El Paso.
Shreveport police Chief Henry Whitehorn Sr. told The Associated Press said his department is working with the U.S. Marshal's Service and other law enforcement agencies to locate Laurean.
"We don't know if he is still in the area," Whitehorn said. "We believe it may have just been a pass through."
The FBI said Sunday that Laurean was also wanted on a federal warrant charging him with unlawful flight to avoid prosecution. Bureau spokesman Newsom Summerlin said that while investigators don't have any reason to believe he's fled the country, that remains a possibility.
Along with the FBI, Brown said federal Marshals, the Naval Criminal Investigative Service and the North Carolina State Bureau of Investigation are hunting for Laurean.
Meanwhile, sheriff's investigators at the scene are spending much of their time on developing evidence, he said.
"While finding him is a main concern, the major concern is that we continue the investigation to clearly find the truth in what happened," he said.
Lauterbach disappeared sometime after Dec. 14, not long after she met with military prosecutors to talk about her April allegation that Laurean raped her. Naval investigators said Saturday the rape case was progressing and Laurean had been under a protective order to stay away from Lauterbach.
Authorities received Laurean's note about the purported suicide from Laurean's wife, whom Brown has said is cooperating with authorities. Her family has described her as "heartbroken."
Lauterbach's mother reported her daughter missing Dec. 19. She had been placed on "unauthorized absence" status by the Marine Corps and was listed that day in a national law enforcement database as a "missing person at risk."
Naval investigators said authorities didn't consider Laurean a threat to Lauterbach, or later a flight risk, because they had indications the pair were on friendly terms. Laurean later refused to meet with investigators and left town without telling his lawyers where he was going.
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Associated Press writer Harry R. Weber in Atlanta contributed to this report.
