They did not identify the suspect, but said he had been wanted on robbery charges in Columbus, Ga. An investigator told WSB that evidence found in the man's car links him to Burk's killing.
Earlier today, Alabama authorities said they would test a gas can recovered in downtown Auburn to see if its contents might have been used to torch a car belonging to a slain university freshman and, if so, whether any DNA evidence was left behind.
Thomas Dawson, assistant police chief in Auburn, said that investigators on the multi-agency task force probing the shooting death of 18-year-old Lauren Burk have interviewed many people about the case and have developed some "promising leads."
Dawson, who also squashed rumors that Burk had been sexually assaulted, distributed photographs of a 2001 Honda Civic similar to Burk's vehicle that authorities hope was seen by someone Tuesday night.
Burk was found 5 miles from the university campus with a gunshot to the head, according to Auburn police. She was transported to a local hospital, where she was pronounced dead. Her car was found engulfed in flames in a campus parking lot a half hour later.
Dawson said an arrest may soon be made but declined to provide additional details.
"I know we're being tight-lipped, but I just think it's the best way to be until we have an arrest in this case," he said. Burk's family released a statement Thursday in which it asked for privacy while expressing gratitude for the emotional outpouring that has followed the teen's slaying.
"The investigation of this terrible tragedy is ongoing, and the Auburn Police Department is doing everything possible to find the person responsible for this horrible act of violence," the family statement reads.
The Burks also directed financial donations to the Lauren Burk Memorial Fund. The money will go toward finding Burk's murderer. Any leftover funds will be given to the Invisible Child, an organization Lauren Burk was involved with that supports starving children in Africa.
Alabama Gov. Bob Riley already offered a $10,000 reward for information leading to an arrest and conviction in the shooting. Georgia Gov. Sonny Perdue, meanwhile, released a statement about Burk's death, as well as the killing early Wednesday morning of Eve Carson, the 22-year-old student body president at the University of North Carolina at Chapel Hill who, like Burk, is from Georgia.
"Georgia is Lauren and Eve's home state, and we will do everything we can to help authorities in Alabama and North Carolina pursue, capture and convict those responsible for their deaths," Perdue said in the statement. He also offered investigators the services of the Georgia Bureau of Investigation.
Auburn police and authorities in Chapel Hill, where Carson was killed, said there does not appear to any investigative link between the two crimes, which were separated by 500 miles and seven hours. The tie instead is the similar shocking impact the killings have had on the respective campuses.
At Auburn, university officials have repeatedly reassured students they are safe. "I want to remind all of you to please be aware of your surroundings at all times, both on campus and off, and if you are traveling at night use the buddy system," Johnny Green, the Auburn dean of students, wrote in a message to students. "We'll continue to be vigilant in our efforts to ensure your safety, but we want you to take that responsibility for yourself, too."
Auburn police have beat back speculation that Burk's slaying might be connected to the unsolved disappearance in June 2006 of 24-year-old Auburn University graduate Lori Ann Slesinski. In that case, the woman's car was found ablaze less than a week after she was reported missing along a road.
A public memorial will be held for Burk, a pregraphic design major and a member of the Delta Gamma sorority, Saturday evening in Georgia. Burk's funeral will follow Sunday, and a vigil will be held at Auburn Monday.
ABC News' Dean Schabner contributed to this report.
