A lawsuit by Delvonn Heckard, 46, alleged that the mayor "repeatedly raped" him when he was a 15-year-old boy. Heckard alleged that Murray had also paid him for sexual acts.
Murray denied the sexual abuse allegations after the lawsuit was filed in April. Subsequently the next month, Murray withdrew from running for re-election in Seattle mayor's race
, saying the campaign should be focused on issues, not the scandal.
Heckard's lawyer filed a motion to withdraw the lawsuit on Tuesday, according to court documents filed in King County.
His lawyer, Lincoln Beauregard, wrote in the motion that his client wanted to "complete his extensive counseling and recovery this December prior to moving forward with this matter."
"Additionally, Mr. Heckard determined that it would be better for the success of his lawsuit, and the citizens of the city of Seattle, for this matter to proceed at a later point in time after Mayor Murray is no longer sitting in power."
Beauregard tweeted that Heckard had decided "to delay the case a few months."
"We, Delvonn and his legal team, will never give up, and never stop fighting," he tweeted.
Mayor: 'It's not true'
On Wednesday, Murray held a news conference with his husband by his side.
"This lawsuit was a painful experience," he said. "As I said when the story first broke, it is not true."
Murray accused Heckard's lawyer of having a "political goal" and said there was a "political effort to end my public career."
The accusations came at a critical time before a primary in August and a general mayoral election on November 7.
This wasn't the first time allegations of sexual misconduct have surfaced during Murray's political career.
In 2008, while Murray was promoting his marriage equality campaign, The Seattle Times reported
that two men accused him of "molesting and raping" them in the 1980s and one of them called reporters and state lawmakers about it.
Murray became mayor in 2014 after 18 years as a state lawmaker. He said he would serve out his term as mayor, which ends in December.
He has not ruled out a re-election campaign as a write-in candidate, reported CNN's affiliate KIRO.