The trial was suspended until Wednesday, Peru This Week reported.
Van der Sloot, a Dutch national and a key figure in the 2005 disappearance of U.S. teenager Natalee Holloway in Aruba, was set to go to trial on murder and robbery charges in the death of Stephany Flores. He could get a 30-year sentence if convicted.
Van der Sloot said he admits much of what is alleged, the Christian Science Monitor reported.
"I want to give a sincere confession, but I don't agree with all the charges that [have been] placed on me by the prosecutor," he said. "Can I have more time to think about this?"
The court had rejected efforts from Flores' family to have the murder charge upgraded to premeditated murder, which carries a life sentence, Radio Netherlands Worldwide reported
Van der Sloot, who allegedly admitted to killing Flores last year, filed a complaint alleging his deportation from Chile -- where he fled following Flores' death -- was unlawful.
In the Holloway case, van der Sloot was the last person seen with the Alabama teen before she disappeared during a vacation to Aruba in 2005. He was arrested twice but police said they were unable to gather enough evidence to charge him.
Van der Sloot faces extortion charges in the United States for allegedly telling the Holloway family he would show them where they could find their daughter's body in exchange for $250,000.