Chicago Fraternal Order of Police Lodge 7 President Kevin Graham said Rush's comment was "wholly baseless and is in fact a slanderous remark which meets the textbook legal definition of defamation."
Rush, 72, made the comments after an April 1 demonstration by members of the union protesting the decision by Cook County State's Attorney Kim Foxx to drop charges against "Empire" actor Jussie Smollett.
Smollett has been accused of faking a hate crime against himself. Foxx has denied claims that Smollett, who is back and gay, received special treatment from her office, and she has ignored calls by various critics to resign.
An NPR-affiliated station in Chicago reported that members of white nationalist groups attended the union's protest, which was also met by counterprotests by members of left-wing groups including the Chicago Alliance Against Racist and Political Repression. A union spokesman issued a statement on Facebook the day after the protest, denying any knowledge of those groups.
"The suggestion, implication, or even correlation that the FOP would in any way associate itself with a racist hate group is a sign of just how biased, malevolent, and extreme the media is in their antipathy toward the police," Martin Prieb said in the post.
"The FOP is the sworn enemy of black people, the sworn enemy of black people,” Rush said Saturday. “The FOP has always taken the position that black people can be shot down in the street by members of the Chicago Police Department, and suffer no consequences."
He added, "I would certainly hope that the FOP and whatever their disagreements may be, whatever concerns that they may have about my ability or leadership, would at least expect the people of their union to not inject racism or white nationalists into the conversation."
"We could not control who showed up for the April 1 protest, just as you cannot control who has shown up to many of your protests throughout your career," Graham wrote to Rush. "We never acknowledged these people, we never encouraged them, and, if they in fact were present, we never gave them any legitimacy. The FOP denounces any hate group regardless of what side of the political fence they sit."
Graham accused Rush, a co-founder of the Black Panther Party's Illinois chapter in the 1960s, of having "fanned the flames of racial division, and made many outlandish and false comments that have encouraged many radical and unhinged people to engage in the most vile and irresponsible speech."
"The comment shows an amazing indifference to our city, a fundamental misunderstanding of the people who keep us safe and a disturbing mendacity," wrote Graham, who noted that 25 percent of the police union's membership is African-American.
"You owe us an apology."
Rush had no immediate response to the letter.