Seattle’s mayor, Ed Murray, said on Tuesday that he would resign, after already announcing in May that he would not seek a second term. Several men have come forward to accuse Mr. Murray of sexually abusing them decades ago, when they were underage.

The announcement came just hours after The Seattle Times published a story with an account by a fifth man, Mr. Murray’s cousin, who said Mr. Murray had abused him in the 1970s.

In a brief statement, Mr. Murray said, as he has many times before, that “the allegations against me are not true.” But he added, “It has also become clear to me that in light of the latest news reports, it is best for the city if I step aside.”

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Mr. Murray, 62, a Democrat, is the city’s first openly gay mayor, and had served in the State Legislature for many years before being elected in 2013. The City Council president, Bruce Harrell, will become mayor upon Mr. Murray’s resignation, which his office said would be effective Wednesday.

An election to replace Mr. Murray permanently is already in full swing, with two candidates — Jenny Durkan, a former United States attorney, and Cary Moon, an urban planner, engineer and local activist — vying to replace him in November.

Mr. Murray expressed gratitude to the city and its residents, saying, “it is important that my personal issues do not affect the ability of our city government to conduct the public’s business.”

Mr. Murray, a liberal progressive, is generally considered a father of Washington’s same-sex marriage law, which he pushed in the State Legislature for years. As mayor, he pushed into law one of the nation’s first big-city, $15-an-hour minimum-wage laws.