Tennis star Billie Jean King, a women's rights activist who has never shied from controversy, acknowledged yesterday at a press conference in Los Angeles that she had a homosexual relationship with her former secretary, who is now suing her for property and lifetime support.

With her husband of 15 years, her parents and her attorney at her side, King admitted that she had an affair with Marilyn Barnett, 32, a former hairdresser who traveled with her as a secretary and "road manager" in the early 1970s.

"I made a mistake, and I'll assume all responsibility for it," said King, who was composed during the 20-minute press conference. She said she called the meeting with reporters, against the advice of her attorney, because she thought it was important to be honest with the public. "I hope they have compassion and understanding," she said.

King denied that she ever promised to Burnett a Malibu beach house that she and her husband own, or other lifetime support, as charged in a "palimony" suit filed on Barnett's behalf this week in Los Angeles Superior Court. King earlier had issued a written statement calling the suit's allegations "untrue and unfounded."

Barnett is now a paraplegic as a result of a fall from the balcony of the Malibu house where she has lived since 1972. It has been reported that Barnett's fall was actually a suicide attempt, but King declined to comment on those reports.

"We have witnesses to testify to facts as we see them," said her attorney, Dennis Wasser, who advised King not to respond to questions about details of her relationship with Barnett.

King yesterday expressed anger and sadness over Barnett's suit, which she said violated her privacy. "I've known for some time that she is unstable, but what can you do?" she said.

"I felt very strongly about this. I've always been above board with the press and I will talk now as I have always talked, from my heart. I've always felt it's important that people have their privacy, and unfortunately someone in my life doesn't think it's very sacred," said King, 37, one of the most outspoken and influential athletes in history.

"I did have an affair with Marilyn, but it was over quite some time ago . . . I'm very disappointed and shocked that Marilyn has done this, not only to herself in a very destructive way but to other people who have cared for her."

Barnett's suit said that she and King became sexually intimate in 1972, approximately six months after they met, and that King promised to give her the Malibu house where they allegedly lived together for a time and to "provide for all of her financial support and needs for the rest of her life."

King emphatically denied yesterday that she had made any such promises. Wasser suggested that Barnett may have filed the suit to gain possession of the Malibu house, from which the Kings have been trying to evict her so that they could sell the property.

"We'll respond to the lawsuit and deny the allegations regarding any contract between the parties," the attorney said.

King arrived at the press conference at an airport holding hands with her husband, Larry, a lawyer, entrepreneur and sports promoter. He introduced her, stressing that forthrightness is one of her essential characteristics and that she insisted on telling her story publicly.

"I've known Bille Jean for 19 years. We met at L.A. State (College).

I love her dearly. I don't think that anything that transpires will change our relationship," said Larry King, who is also named in Barnett's suit.

Resting her head on his shoulder as she answered questions, Billie Jean said: "I want to thank Larry and my parents for standing by me. I now know who my friends are." She referred to Larry as "my husband, my lover and best friend," and said: "In some ways, I think we're closer today than we've ever been, and our marriage is stronger."

King, who has won 12 Grand Slam singles titles and earned the No. 1 U.S. ranking seven times during a 20-year competitive career, helped engineer the split of women's pro tennis from the men's game in 1971 and was the driving force in establishing the women's tour as an artistic and commercial success.

King said yesterday that she hopes her fans "try to understand" her revelations, but that she is most concerned about her family and friends.

Her parents drove home to Long Beach, Calif., immediatley after the press conference. "It was a very difficult day on the family, but we're behind her 100 percent," said Bill Moffitt, King's father, a retired fireman, in a telephone interview. "We support her all the way. We wouldn't be much of a mother and father if we didn't, would we?"

Moffit said that Wasser had advised the family to make no further comment. King planned to leave directly from the press conference and catch a flight to Tokyo, where she is playing in a doubles tournament next week, Moffit said.