The Dutch government said Interpol has issued an international arrest warrant for Van der Sloot.
Guardia said the 22-year-old Dutchman, who was in the country for a poker tournament, appears with the young woman in a video taken at a Lima casino early Sunday.
The victim's father, Ricardo Flores, told reporters she was killed about 8 a.m. in a hotel room in the upscale Miraflores neighborhood that was splattered with blood, indicating a struggle.
The killing occurred exactly five years after the May 30, 2005, disappearance of Holloway in Aruba, a Dutch Caribbean island.
Van der Sloot left Peru on Monday, Guardia said, according to immigration registry. He had been staying at the hotel since May 14 and checked out on Sunday four hours after he arrived there with the victim, the police general added.
"We have an interview with a worker at the hotel who says she saw this foreigner with the victim enter his room," said Guardia.
Interpol has issued an international arrest warrant for Van der Sloot, Dutch Foreign Ministry spokesman Bengt van Loosdrecht told The Associated Press in The Netherlands.
He cited as his sources Peruvian police and the Dutch Embassy in Lima. The embassy's head of consular affairs, Angela Lowe, told the AP she could not comment on the case.
An attorney for Van der Sloot in New York City, Joe Tacopina, said he did not know his client's whereabouts and has not been in touch with him since the Peru allegations emerged.
Tacopina cautioned against a rush to judgment.
"Joran van der Sloot has been falsely accused of murder once before. The fact is he wears a bull's-eye on his back now and he is a quote-unquote usual suspect when it comes to allegations of foul play," Tacopina said.
Van der Sloot was twice arrested but later released for lack of evidence in the 2005 disappearance of Holloway, who was on a high school graduation trip to the Caribbean island.
No trace of her has been found and van der Sloot remains the main suspect in the case, said Ann Angela, spokeswoman for the Aruba prosecutor's office.
"What's happening now is incredible," she said. "At this moment we don't have anything to do with it, but we are following the case with great interest and if Peruvian authorities would need us, we are here."
Van der Sloot's late father was a prominent judge in Aruba.
The mystery of Holloway's disappearance has garnered wide attention on television and in newspapers in Europe and the United States.
Two years ago, a Dutch television crime reporter captured hidden-camera footage of Van der Sloot saying he was with Holloway when she collapsed on a beach, drunk.
He said believed she was dead and asked a friend to dump her body in the sea.
Judges subsequently refused to arrest van der Sloot on the basis of the tape.
A spokeswoman for Holloway's mother, Beth Twitty of Mountain Brook, Alabama, told the AP the family was aware of the development in Peru but would have no comment.