Police said Friday they had strong leads in the mysterious off-campus shooting death of an Auburn University freshman, but have yet to make an arrest as the slain woman's parents announced the creation of a fund in honor of Lauren A. Burk.

"We have some strong leads, promising leads, and I hope to be standing before you soon with some good news," Auburn Assistant Chief of Police Tom Dawson said at a press conference Friday.

Burk, 18, was found wounded on Alabama Highway 147 around 9 p.m. Tuesday, about three miles off campus, and Auburn police said her Honda Civic was discovered engulfed in flames at the campus about 20 minutes later. She was taken to East Alabama Medical Center, where she died Tuesday night.

Dawson gave few details in the case during the brief press conference, saying the student had not been sexually assaulted and announcing the discovery of a gas can in downtown Auburn, which is being tested for DNA. Police believe a petroleum-based accelerant was used to set Burk's car on fire.

Officials are asking the public to call police if they had seen a 2001 Honda Civic matching Burk's in the Auburn area on the night of her death.

"We have an obligation to the citizens of Auburn and to the Burk family," Dawson said. "I know we're being tight-lipped, but I just feel that's the best way to handle this issue until we have an arrest in this case and at that time we'll get into all the details and let you know."

Authorities will continue beefed up patrols of campus until Burk's killer is found, he said.

"Their [staff and students'] safety is of our utmost concern," he said. "We continue to have extra patrols on Auburn University campus, and we will continue to do so until this case is brought to a conclusion."

Meanwhile, the Burk family asked for privacy Friday as they announced the creation of the Lauren Burk Memorial Fund. Donations can be made at any Wachovia Bank "to help apprehend the person responsible for her death," the family said in a statement.

"The family of Lauren Burk would like to express their gratitude for all the kindness and prayers expressed during this tragedy," the family's statement said. "They respectfully ask for privacy during this time so they may grieve for their great loss, as well (as) celebrate Lauren's life."

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Georgia Gov. Sonny Perdue said he has asked the Georgia Bureau of Investigation to offer assistance in the investigations.

Perdue said in a statement that he and his wife "are deeply saddened by the senseless, tragic murders of these two bright and talented Georgians. We are praying for their families and friends as well as the campuses and communities that are mourning these painful losses."

In a separate case, another Georgia college student — this one from the University of North Carolina at Chapel Hill — was also shot in the head and killed this week.

Student body president Eve Marie Carson, 22, was found dead on Wednesday. Authorities and school officials identified her as the shooting victim on Thursday.

Marietta, where Burk was from, and Carson's hometown of Athens are about 67 miles apart.

"I don't have anything at this point to indicate that this is related," Dawson said Thursday. "I've had my investigators contact authorities there, but there's nothing to connect the two cases."

A $10,000 reward was offered in the Burk case by Alabama Gov. Bob Riley's office.

"Everything that can be done must be done to bring this killer to justice," Riley said in a statement Thursday.

Riley said he hopes the reward will "encourage someone who can help police solve this crime to come forward. Our prayers go out to Lauren's family and friends during this difficult time."

His second-in-command said the governor's office wanted answers as soon as possible.

"We hope we can resolve this as quickly as we can," Lt. Gov. Jim Folsom told FOX News on Thursday. "This is a real shock to the state of Alabama and the Auburn community."

Folsom said he couldn't offer much in the way of specifics about the crime.

"Details are sketchy," he said.

On Thursday, students held a prayer vigil in Burk's honor.

"We are all family here," organizer Shaemun Webster told MyFOXAL.com. "So we've come tonight to bring a connection through prayer for healing."

The teen's sorority sisters from Delta Gamma and other friends mourned her Thursday, describing the Marietta, Ga., native as sweet, friendly and well-liked and saying they have no idea who would have wanted her harmed.

"Considering the unexpected and disturbing nature of the situation, the women of Delta Gamma have reacted with immense concern," the sorority's national office said in a statement. "Delta Gammas across the country offer hope and friendship to Lauren's family and all who have been affected by this tragedy."

"I can't imagine someone she knew doing this to her," Burk's close friend Jay Seyfried, a classmate from Walton High School, told MyFOXAtlanta.

Auburn Campus reacts to killing of Lauren Burk

University officials advised students in an e-mail around noon Wednesday that there was "no indication of additional danger to campus or student safety." But the school said the police presence on campus had been increased.

"As soon as we know more we might release it, but what information we have now we're holding it close to our chest," he said.

Burk's death has stunned the Auburn campus in Lee County, Ala., where the mood was subdued and students walked around mostly in pairs, according to MyFOXAtlanta.com.

"It's just really scary knowing I came here, feeling safe here on this campus," Auburn student Katrina Kreimer told the news station.

Sophomores Darious "Slim" Merchant, 20, and Charles Daniels, 19, said they had not seen much change in the atmosphere on campus, although they have noticed more female students riding shuttle buses at night instead of walking.

"That makes sense," Merchant said.

Two memorials will be held for the slain student over the weekend and a campus-wide memorial service for Burk is scheduled for Monday afternoon.

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The Associated Press contributed to this report.