Twelve white male San Francisco police officers who were passed over for promotions are suing the city for race and sex discrimination, led by a lieutenant whose similar suit 16 years ago netted a $1.6 million settlement. A 13th plaintiff, now retired, says she was denied promotion because she is a white lesbian.

The lawsuit, filed Tuesday in federal court, is the latest round of a conflict that dates back at least to 1973, when an organization representing black and female officers sued the San Francisco police force for discrimination in hiring and promotions. The city settled the case in 1979 by taking steps to increase diversity, including the “banding” of promotional test results so that all candidates who scored within a certain range were treated the same, allowing them to be judged on other factors such as experience and language skills.

Federal courts upheld banding in 1992 in the face of a lawsuit by the San Francisco Police Officers Association, which argued that the practice discriminated against whites.

The U.S. Justice Department reviewed the Police Department in 2016 and commended it for the increased diversity in its workforce — with nearly 49% nonwhites and 15% women, both above national averages — but said improvements were still needed, particularly in promotions.

But the 1979 settlement with minority and female officers expired in 1998, and Tuesday’s suit is the latest to claim that the department’s continuation of its test-scoring policies is both unfair and illegal.

“The city — to this day — has a long-standing practice and custom of discriminating against white males in SFPD promotions to the rank of sergeant, lieutenant and captain,” the officers’ attorney, M. Greg Mullanax, said in the lawsuit.

For example, he said, in the 2016 promotional exam for lieutenant, banding was used to promote all three black sergeants who applied, even though their scores were lower than those of 11 white candidates who were denied promotions. A similar procedure was used to promote four women, while passing over seven men with higher scores “so the Police Department could accomplish its gender-biased agenda,” the suit said.

The lead plaintiff, Lt. Ric Schiff, was denied a promotion to captain in favor of women and minority candidates with lower scores, the suit said. Schiff, 59, an officer since 1985, was the lead plaintiff in a 2003 lawsuit on behalf of 12 sergeants who accused the police force of discriminating in favor of black candidates for lieutenant by banding the top 97 test scores and bypassing white, Latino and Asian American officers with higher scores.

The city, without any acknowledgment of wrongdoing, settled the lawsuit for $1.6 million, giving $200,000 to Schiff, who was later promoted to lieutenant.

Mullanax said the Police Officers Association contacted Chief Bill Scott about the issue, and some of the officers who were denied promotions met with Scott to air their concerns, but none received any “substantive response.” The suit seeks court-ordered promotions for the plaintiffs and damages, including punitive damages against Scott and his predecessor, Greg Suhr.

John Coté, a spokesman for City Attorney Dennis Herrera, said the Police Department “uses lawful, merit-based civil service examinations in making promotions.” The system, he said in a statement, is “designed to provide qualified individuals with the chance for advancement while ensuring fair treatment without regard to race, gender, religion, age or other status.”

Bob Egelko is a San Francisco Chronicle staff writer. Email: begelko@sfchronicle.com Twitter: @BobEgelko