"This is entirely behind me," Weiner said at an evening news conference, hours after the gossip website The Dirty posted X-rated text messages and a crotch shot that it said the former congressman exchanged with a woman after he left office.
Weiner admitted sending a woman sexually explicit photos and messages and acknowledged the activity took place as recently as last summer, more than a year after he resigned from the House in disgrace for the same sort of behavior with at least a half-dozen women.
But with his wife, Huma Abedin, smiling shyly an arm's length away from him, he said: "I want to bring my vision to the people of the city of New York. I hope they are willing to still continue to give me a second chance."
Weiner then turned the microphone over to his wife, who did not appear with him at the June 2011 news conference when he stepped down from Congress over a scandal that began with a Twitter photo of his bulging underpants.
This time, Abedin reaffirmed her support for her husband and said the sexting matter is "between us."
"I love him, I have forgiven him, I believe in him, and as we have said from the beginning, we are moving forward," said Abedin, a longtime adviser to former Secretary of State Hillary Rodham Clinton.
Abedin said her husband had made some "horrible mistakes both before he resigned from Congress and after" but insisted the two of them discussed "all of this" before he jumped into the mayor's race in May.
On Tuesday, Harper's Bazaar released an excerpt from a piece Abedin wrote explaining that although she doesn't like the limelight, she decided to campaign for him because he's "a better man" now.
The latest disclosures could severely test voters' willingness to forgive Weiner, who has said he spent his two years in political exile since the scandal trying to make things right with his wife and earn redemption.
Three of his rivals for mayor immediately called on him to drop out of the race.
The 48-year-old Democrat has been near the top of most polls since his late entry into the campaign.
"I said that other texts and photos were likely to come out and today they have," said Weiner, who added that he was surprised that more had not previously surfaced.
After the news conference, Weiner went directly to a mayoral forum on gay men's issues and was warmly received.
The woman with whom he exchanged the messages was not identified by The Dirty. She told the website that she was 22 when she began chatting with Weiner on a social networking site. She said their online relationship began in July 2012 and lasted six months.
She said that Weiner used the alias "Carlos Danger" for their exchanges but that she knew she was talking to the former congressman.
The exchanges posted on The Dirty consist of sexually explicit fantasizing about various sex acts. At one point, the man reported to be Weiner wrote, "I'm deeply flawed."
The woman said Weiner promised to help her get a job at the political website Politico and suggested meeting in a Chicago condo for a tryst.
The woman said she and Weiner also exchanged nude photos of themselves and engaged in phone sex. The Dirty ran a pixelated photo of what it said were Weiner's genitals.
"This was a bad situation for me because I really admired him. Even post scandal, I thought he was misunderstood. Until I got to know him. I thought I loved him. Pretty pathetic," the woman was quoted as telling the website.
She said he later asked her to destroy the evidence of their chats. She insisted that she never had sex with Weiner or received any payment from him.
The woman said her relationship with Weiner "fizzled" in November 2012. She said she last heard from him this past April, when his intention to run for mayor was revealed in a New York Times Magazine profile.
Weiner said that not every allegation made by the woman was true but that he was not going to dispute specific claims. The lawyer for The Dirty's founder, Nik Ritchie, said his client was ill and would not comment Tuesday.
Weiner said his last sexting exchange happened "sometime last summer, I think," after he and his wife sat down for a glowing People magazine profile in which they said their troubles were behind them.
Abedin, who was pregnant when the original sexting scandal broke and gave birth months later, has played a large and visible role in his mayoral campaign.
Two weekends ago, she walked hand-in-hand with Weiner as they talked to voters on a Harlem street.
Three of his rivals for mayor - Public Advocate Bill de Blasio and former City Councilman Sal Albanese, both Democrats, and billionaire John Catsimatidis, a Republican - called on Weiner to quit the race.
"Enough is enough," de Blasio said. "The sideshows of this election have gotten in the way of the debate we should be having about the future of this city."
Another mayoral hopeful, city Comptroller John Liu, stopped short of calling for Weiner to bow out, but suggested his "propensity for pornographic selfies is a valid issue for voters."
The other leading Democratic candidates, including City Council Speaker Christine Quinn and former City Comptroller Bill Thompson, did not immediately comment.
The disclosure suddenly puts Weiner's indiscretions, judgment and candor back in the forefront of his campaign, political analysts said.
"It makes it tougher to believe this is behind him," said Democratic former state Assemblyman Michael Benjamin, now a political consultant.
Some voters have said they felt Weiner had atoned for his past and were willing to give him a second chance. But a third chance, for misbehavior that occurred after his resignation?
"I think he had a chance to redeem himself and if he did it twice, he really betrayed the public's trust again," said Jeremy Green, a New Yorker. "I think he's past the point of no return for New Yorkers."
Associated Press writers Jennifer Peltz, Meghan Barr, Jacob Pearson and Deepti Hajela contributed to this story from New York.