Four other men publicly claim Murray abused them as minors. Dyer claimed he would try to avoid being molested by pretending to sleep-which didn't stop Murray from abusing him.
A Democrat, Murry is the first openly gay mayor of Seattle.
City Councilmember Bruce Harrell will become mayor and will decide within five days whether to fill out the remainder of the term, the statement says. Two candidates - Jenny Durkan and Cary Moon - are campaigning to succeed him in the November 7 election.
This was after a child welfare report was filed in the state of OR with the claims.
"I think this fifth, sixth victim who is a family member who says, 'Enough is enough, ' has got to hit people in the heart". I have always wished him well as mayor even when I disagreed with his policies. I called on the mayor to resign this morning.
The mayor has vehemently denied all of those accusations, at times suggesting that they were politically motivated, and refused repeated calls to step down, but in May said he would not seek re-election.
"The City must focus on governance and day-to-day business without distraction", Harrell said. "I have a plan in place for a seamless transition in order for City operations to continue at the highest standard". "Unfortunately, we know that there is another victim because I know that there are several more victims that haven't come forward".
In April, a 46-year-old man sued Murray, claiming the mayor paid the man for sex when he was a homeless, drug-addicted teenager in the 1980s.
'It is time for Mayor Murray to step down, ' Durkan said in a new statement.
During his time in office, Murray promoted a number of progressive causes, including defending Seattle's sanctuary city status, launching a campaign to push the city's minimum wage to $15 an hour, fighting for same-sex marriage, and vociferously opposing President Donald Trump's immigration policies.
Jenny Durkan accepted Murray's endorsement before the primary.
"I feel victory, but saddened that it required another victim to come forward for him to resign", another accuser, Lloyd Anderson, said in a statement.
In 1984, an Oregon Child Protective Services caseworker determined that Murray abused a child in the foster system, though no criminal charges were filed.
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