His wife stood by his side and also spoke with reporters on Tuesday. Weiner said his wife has given him a second chance and he's asking New York City voters to do the same.
The primary is 49 days away. With no intention of dropping out of the mayoral race, Weiner addressed the latest leak of x-rated material. The website "TheDirty.com" posted a series of explicit messages and a picture Weiner allegedly sent to a 22-year-old woman last summer, about a year after he resigned his seat in the House.
"While some of the things that have been posted today are true and some are not, there is no question that what I did was wrong. This behavior is behind me. I've apologized to my wife," Weiner said.
Weiner said his wife, Huma Abedin, was aware of what the rest of the world is just now learning. The woman claims Weiner used the alias "Carlos Danger" to chat with her on the social networking site Formspring. She says they exchanged nude photos and had phone sex. She said their online relationship began in July 2012 and lasted six months.
Weiner's wife said they have spent a lot of time in therapy and she loves and forgives her husband.
"It was not an easy choice in any way, but I made the decision that it's worth staying in this marriage," Abedin said. "That was a decision I made for me, for our son, and for our family."
In 2011, then-Congressman Weiner admitted he had sexual conversations with at least half a dozen women. The scandal first came to light when Weiner tweeted a close-up picture of himself in his underwear to a Seattle woman. He later resigned.
Weiner said he and his wife knew more photos and texts would surface if he chose to run for mayor of New York City, but they decided to move forward with the campaign.
"I want to bring my vision to the people of the city of New York," Weiner said. "I hope they're willing to still continue to give me a second chance and I hope they realize that, in many ways, what happened today was something that frankly had happened before, but it doesn't represent all that much that is new."
Tuesday was the first time Weiner's wife spoke during a news conference. She said her husband made some horrible mistakes before and after he resigned from Congress, but she said that's between them and their marriage.
Three of Weiner's 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.
The Associated Press contributed to this report.