Police also released a composite sketch of a suspect.
Audrey Seiler, 20, was cooperative during the interview, conducted one day after she was found in a marsh less than two miles from her apartment, police spokesman Larry Kamholz said. He said authorities had no reason to doubt her claim that she had been kidnapped.
Police have released few details in the case. Assistant Police Chief Noble Wray said authorities have not drawn any conclusions about what might have happened after Seiler vanished from her off-campus apartment early Saturday without her coat or purse.
Police won't say how Seiler broke free or much else. With so many unanswered questions, there's been speculation in the community that this could be a hoax, reports CBS News Correspondent Jennifer Donelan.
In a Thursday evening press conference, Wray said a search of the area where Seiler was found did not yield a suspect.
"Like in any other major investigation, there may be inconsistencies, but we are continuing with the investigation," Wray said.
He added it is not the role of a police department to speculate on the outcome of an investigation before it's complete.
Wray said police waited a day to conduct an in-depth interview to "give her time to refresh, time to spend with her family."
Police have declined to say whether Seiler was sexually assaulted. She was treated at a hospital Wednesday and released after less than six hours. A doctor said Seiler was cold and dehydrated and had muscle aches.
Her discovery capped an intense search in which dozens of volunteers from Seiler's hometown of Rockford, Minn., slogged through marshes and woods around campus and investigators scoured phone records and apartments for clues.
Seiler was involved in another mysterious incident Feb. 1, when she told police that someone struck her from behind and knocked her unconscious. She told police that she was then moved about a block from where she was attacked but was not sexually assaulted or robbed, authorities said.
Police are unsure if there was any connection between the Feb. 1 attack and Seiler's disappearance, which was a shock to people in Rockford, even though it happened so far away.
Police refused a request by The Associated Press to release the police report from that incident. Capt. Richard Bach said officers believe the information might be connected to the latest investigation.
Police are searching for a white male in his late 20s or early 30s, approximately six feet tall, wearing a black sweatshirt, jeans and a black cap, and possibly armed with a gun as well as a knife, reports CBS News Early Show National Correspondent Jon Frankel.
"Audrey reports that she was abducted at knife point," said Wray.
Officer Shannon Blackamore said Seiler did not know the abductor. He also said there was an indication or threat of a gun, though Seiler never saw the weapon.
"Audrey reports she was not free to leave and was not injured," Blackamore said.
Seiler was treated at a hospital and released after being there less than six hours. Dr. Philip Schultz said Seiler was cold and dehydrated and had muscle aches as a result of being confined.
Other than that, "according to the doctors, she was in good condition," Wray told CBS News. "When we talked to her yesterday, she appeared to be in good physical condition."
Her discovery capped an intense search in which dozens of volunteers from Seiler's hometown slogged through marshes and woods around campus and investigators scoured phone records and apartments for any clue into the disappearance. Police used dogs, planes and boats in the search.
Officer Larry Kamholz said Seiler was found after an employee at a nearby office building called police to report what she thought was a body in the marsh less than two miles from Seiler's off-campus apartment.
Officers with weapons drawn searched the heavy brush, and a helicopter with heat sensors was brought in to aid the search.
Rejoicing residents took to the streets to tear down missing-person posters in Seiler's hometown of Rockford, Minn., a small town about 30 miles west of Minneapolis.
"Right now it's just an unbelievable feeling," said Roman Pierskalla, principal of the high school in Rockford. "Today, the prayers of everyone in the Rockford community have been answered."
Later, a candlelight vigil turned into a celebration; a local Domino's sent free pizzas and the Rockford Fire Department brought a ladder truck that hoisted an American flag.
Seiler was last seen on a surveillance tape from her apartment building early Saturday. She apparently left without her car or any personal belongings, and her door was left open.
For many in the Midwest, the Seiler case brings back the trauma of the disappearance of another Minnesotan: University of, kidnapped last November from a shopping mall in Grand Forks, North Dakota.
Police have said that they believe Sjodin, 22, of Pequot Lakes, Minn., is dead. Alfonso Rodriguez Jr., 51, of Crookston, Minn., was charged with her kidnapping charges after police said traces of Sjodin's DNA were found in blood in his car.
Police also found one of Sjodin's shoes, elsewhere, a few days after her disappearance. But her body has not been found.