Assistant District Attorney Joann Risse said prosecutors would waive three of the five child pornography possession charges against him if he pleaded guilty on two remaining charges.
Karr, 41, would get credit for time served, would be placed on probation for three years and would be required to register as a sex offender.
Defense lawyer Robert Amparan said he would discuss the deal with Karr, but said he still believes his client is innocent.
Amparan said the public had received a "false picture" of Karr, whom he described as a "Southern gentleman with a sense of humor."
Karr's bail was set at $200,000, after Judge Cerena Wong called him a flight risk. Karr spent several months in the Sonoma County jail in 2001 awaiting trial on the child porn charges and fled after being released.
Amparan would not say whether his client could afford bail but said Karr would remain behind bars for now.
Karr "made a bad decision in a moment of desperation" when he fled before his 2001 trial but now stands prepared to face the charges against him, Amparan said in court, arguing that Karr should be released from custody without having to post bail. Karr no longer possesses a passport, he noted.
"We still feel that Mr. Karr will ultimately be exonerated," Amparan said, adding that Karr has never been convicted of a crime. "There is no reason to run."
Karr, a schoolteacher, was arrested Aug. 16 after making phone calls and writing e-mails suggesting he killed Ramsey, a 6-year-old beauty queen, in her Boulder, Colorado, home in December 1996. He was returned to the U.S. from Thailand only to have the Ramsey case collapse.
DNA tests failed to connect Karr to the crime, and investigators had no evidence he was even in Boulder at the time of the slaying.
L. Lin Wood, the attorney who has represented JonBenet's family for seven years, told CBS News' The Early Show that if any good came out of the Karr fiasco, it was to reinforce DNA as the key to eventually solving the case.
"I think the public was finally informed that this is a case that will be, in all probability, solved by DNA. There were a lot of misconceptions early in the Ramsey case that the DNA was not quality or somehow degraded or contaminated," Wood said.
Before making the plea offer, Risse argued against releasing Karr.
"This defendant represents a potential threat to the children of this community," she said.
When he was arrested in 2001, Karr was in possession not just of the alleged child porn images but also "numerous writings that revealed his pedophilic tendencies," Risse said.
Amparan countered that the charges Karr was facing contained no direct allegations of pedophilia and that prosecutors had no grounds for making such accusations.
Karr appeared subdued in court, sitting between his two lawyers in his blue jail uniform, head bowed. He did not speak during the hearing.
Amparan told the court that Karr's notoriety has forced his jailers to keep him confined to his cell for 23 hours a day as a safety precaution to avoid harassment by other inmates. Amparan said he would file a motion requesting that Karr not be required to appear personally at his trial to spare him the intense public attention surrounding the case.
Karr's trial is set to begin Oct. 2.