CHICAGO — A federal judge on Thursday sentenced R. Kelly to 20 years in prison for child sex crimes, after a jury found that he had produced three videos of himself sexually abusing his 14-year-old goddaughter.

In a victory for the defense, the judge ruled that all but one year of the prison sentence would be served at the same time as a previous 30-year sentence that Mr. Kelly received after a jury in Brooklyn convicted him of racketeering and sex trafficking charges.

The jury in Chicago convicted Mr. Kelly, 56, of six of the 13 charges brought against him, including three counts of coercing minors into sexual activity and three of producing sex tapes involving a minor. He was acquitted of a charge that he had attempted to obstruct an earlier investigation into his abuse of the goddaughter, and two other counts of enticing minors to have sex.

Federal prosecutors had argued that Mr. Kelly deserved 25 years in prison on top of his earlier sentence, citing the singer’s “lack of remorse” as a reason he would pose a danger to society if released.

“The only way to ensure he will not reoffend is to impose a sentence that will keep him in prison for the rest of his life,” Jeannice Williams Appenteng, one of the prosecutors, said in court on Thursday.

A lawyer for Mr. Kelly, Jennifer Bonjean, argued that her client was “likely to die in prison either way,” but that if he did not, he would not pose a threat in old age. She is appealing the convictions in both Brooklyn and Chicago.