In April, Murray was accused in a civil lawsuit of
sexually abusing a teenage boy about 30 years ago.
Murray, who was elected in 2014 after 18 years as a state lawmaker, said, "The allegations against me are not true. But the scandal surrounding them and me is hurting this city."
He told reporters the race should be about issues such as homelessness, the city's growth and livability, and on equitability and affordability.
"The mayor's race must be focused on these issues, not on a scandal, which it would be focused on if I were to remain in this race."
The mayor was accused in a lawsuit by Delvonn Heckard, now 46, who said the mayor "repeatedly raped" him when he was a 15-year-old boy and the mayor was 32. Heckard says Murray, now 62, also paid him for sexual acts.
The lawsuit also alleges that Heckard was not the only child abused by the mayor. "On at least one occasion, D.H. was at Mr. Murray's home when another apparently under aged boy was at the apartment. D.H. was of the understanding that Mr. Murray was having sex with the other boy for money at the same time," the complaint reads.
Mayor will continue to serve
The mayor told people gathered for the announcement that he will serve out his term, which ends in December.
He was flanked by supporters, including his spouse, who hugged him when the mayor singled him out for thanks.
He took no questions from reporters, and later tweeted: "Serving you as mayor of the city I love has been the honor of a lifetime."