In a video posted on his campaign website Tuesday night, Weiner vowed to fight on.
"Quit isn't the way we roll in New York City," Weiner said in the spot, filmed in his apartment Saturday. He added, "Someone wants to come out with something embarrassing about you in your private life, you gotta talk about that for a little while."
His wife, Huma Abedin, does not appear in the video.
Abedin, who has stood by him through the first and second waves of his sexting scandal, is a longtime aide to Hillary Clinton -- the former first lady, U.S. senator and secretary of state seen as a possible 2016 presidential contender. Former President Bill Clinton officiated at the couple's wedding.
The Clintons have not publicly commented on Weiner's bid for mayor, which has been reeling since revelations of his online exchanges with as many as 10 women -- including three relationships after such escapades forced him to resign from Congress.
A longtime close associate of the former first couple voiced confidence Tuesday that they are "deeply displeased" with Weiner's candidacy. "The person they'd be concerned about is Huma," said the source, who hasn't heard from the Clintons directly.
The source also said the Clintons would not take their disapproval public, but declined to speculate whether they would privately make their feelings known to the Weiners.
Asked Monday night whether he would leave the race if the Clintons urged him to, Weiner responded, "I am not terribly interested in what people who are not voters in the City of New York have to say." The Clintons live in Westchester County.
Weiner softened his tone Tuesday morning after an upper Manhattan mayoral forum.
"Let me make it very clear, I've got an enormous respect for the Clintons," he said. "They've been enormous friends, to my wife and my family. There should be no intent to disrespect.
"But what I've been trying to make clear is that what is important to me in this race is the ideas that animated me to run."
Meanwhile, Sydney Leathers shared graphic details of her cyber-relationship with Weiner on Howard Stern's satellite radio show. Leathers, 23, who came forward last week, depicted Weiner as having an insatiable appetite for phone sex.
Weiner, in a Daily News interview published Tuesday, was asked if he feared another ex-sext partner may surface. He replied:
"These are people who I thought were friends, people I trusted when I communicated with them. But who knows what they might do now?"
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