Murray in a statement said he will step down on Wednesday at 5 p.m. local time. Seattle City Council President Bruce Harrell will become acting mayor.
“While the allegations against me are not true, it is important that my personal issues do not affect the ability of our city government to conduct the public’s business,” said Murray in a statement.
Seattle voters elected Murray as their city’s mayor in 2013. The openly gay Democrat had previously been in the Washington Legislature.
Murray in May announced he would not seek re-election after a fourth man came forward to allege he paid him for sex when he was a teenager in the 1980s. Media reports indicate Murray’s cousin on Tuesday accused him of molesting him on Long Island, N.Y., in the 1970s.