8:31 AM PT -- Sources close to R. Kelly tell TMZ that Williams' attorney tried to shake down the singer prior to filing the lawsuit. In a letter sent to R. Kelly's legal team -- obtained by TMZ -- Williams' attorney, Jeff Deutschman, says R. Kelly's lawyers should contact him if they want to resolve the matter outside of court. Deutschman also writes that no response from R. Kelly's camp would result in the lawsuit being filed.

Clearly, they didn't come to terms.

R. Kelly is now facing a lawsuit from a new accuser who says he sexually abused her when she was 16 years old.

Heather Williams filed the suit in Cook County, Illinois ... and in the suit, she says she met R. Kelly in late May of 1998 while she was walking down a street in Chicago. She says the singer was driving by, and stopped and spoke to her ... then sent his people to meet her and her family at a restaurant.

According to the docs, obtained by TMZ, R. Kelly's associate told Heather and her fam ... that R. Kelly wanted her to come to her studio and appear in one of his videos. She admits she was "starstruck."

She claims in June, R. Kelly began sexually abusing her. She's not specific about where it happened but says they had sexual intercourse and oral sex. In her suit, Heather says the sexual abuse continued until she was an adult.

Heather says she was seeing a therapist in June 2015 when she "broke through her repressed memory" and could finally speak about the alleged abuse. She says she's suffered shame, guilt, self-blame and depression -- and she's suing the singer for at least $50,000.