"I didn't commit any crime, and I didn't do any harm," Condit told the D.C. Superior Court, according to McClatchy Newspapers and The Associated Press.
Levy, 24, disappeared May 1, 2001. Her remains were found in the park a year later.
In the months after Levy's death, Condit, D-Calif., quickly came under scrutiny after reports that he and the intern were involved in a sexual relationship. He was never charged in the case and he never admitted an affair, but the scandal torpedoed his political career.
"From the beginning of this case, you have lied," public defender Maria Hawilo said as she cross-examined Condit, according to The Washington Post.
Hawilo asked the ex-congressman whether he had an intimate relationship with Levy. Condit responded, "I'm not going to respond to those types of questions, based on my privacy and Chandra's privacy."
Hawilo repeated the question, but Superior Court Judge Gerald I. Fisher told her to move on, McClatchy reported.
Speaking with Assistant U.S. Attorney Amanda Haines, Condit said he has never divulged whether he and Levy were intimate.
Condit's daughter, Cadee, watched her father testify, as did Levy's mother, Susan, who took occasional notes, the AP reported.
Guandique was charged with Levy's murder in 2009. Prosecutors say he has a history of sexually assaulting female joggers in Rock Creek Park.
The trial could last a month.