According to the report, Weiner used an anonymous handle to carry on a sexually explicit online relationship with the woman for six months after resigning in disgrace from Congress.
During the press conference, Weiner said that the sexting scandal, "Caused many stresses and strains in my marriage, but I'm pleased and blessed that she's given me a second chance, and I'm asking New Yorkers to give me a second chance."
As for the timeline as to when this most recent sexting incident took place Weiner said, "Some were before, some happened after, but the fact is that was the time we were working through some things in our marriage."
Weiner also said that he and his wife expected more of these texts to come out and that she knew everything.
His wife, Huma, not only stood by his side, but she stepped up to the podium to make a surprise statement of her own.
She said, "It was the beginning of a time in our marriage that was very difficult and it took us a long time to go through it," and continued, "It took a lot of work and a whole lot of therapy to get to a place where I could forgive Anthony."
Abedin stated that "horrible mistakes" were made both before and after he resigned from Congress, but that those things were between the two of them and in their marriage.
She ended with, "I love him, I have forgiven him, I believe in him, and as I have said before, we are moving forward."
Weiner, who resigned his House seat in June 2011 after acknowledging having sexual conversations with at least a half-dozen women, has been near the top of most mayoral polls since his late entry into the race this spring.
In a statement released earlier Tuesday by Weiner's office, the Democratic candidate for mayor says these issues are behind him.
"I said that other texts and photos were likely to come out, and today they have. As I have said in the past, these things that I did were wrong and hurtful to my wife and caused us to go through challenges in our marriage that extended past my resignation from Congress," he wrote. "While some 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 Huma and am grateful that she has worked through these issues with me and for her forgiveness. I want to again say that I am very sorry to anyone who was on the receiving end of these messages and the disruption that this has caused. As my wife and I have said, we are focused on moving forward."
Weiner has been at or near the lead in recent polls in the Democratic race for mayor as he tried to push questions about his integrity behind him.
TheDirty.com claims that Weiner exchanged sexually explicit photos with the woman. and they participated in sex chats.
The woman, who is not named in the report, is quoted as saying, "I was 22 and in a bad place, but if anyone asked him he would say the same thing about himself, yet he's an adult. 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."
According the report, Weiner used the handle "Carlos Danger" to communicate with the woman.
You can read the full story on thedirty.com. Warning: some of the material is graphic. Eyewitness News has not independently confirmed the details of their story.
Weiner's wife, Huma Abedin, has played a large - and increasing - role in his mayoral campaign.
Abedin, a longtime adviser to Hillary Rodham Clinton, urged Weiner to run for office, has led his campaign fundraising and recently made her debut on the campaign trail. Two weekends ago, she walked hand-in-hand with Weiner as they talked to voters on a Harlem street.
Weiner's political rivals were already calling for him to drop out of the race.
"The sideshows of this election have gotten in the way of the debate we should be having about the future of this city. And yes, I'm talking about Anthony Weiner," Democrat Bill de Blasio said. "Enough is enough. I'm calling on Anthony to withdraw from this race - for the good of the city that I know he loves as much as all of us."
Weiner's original problems began on May 28, 2011, when a website run by conservative commentator Andrew Breitbart posted a lewd photograph of an underwear-clad crotch and said it had been sent from Weiner's Twitter account to a Seattle woman.
Weiner denied that he sent the photo, claiming that his Twitter had been hacked.
But after more women came forward and more photographic evidence emerged - some of it X-rated - Weiner admitted that he had lied. Abedin was not at his side when he announced his resignation.
He then entered two years of self-imposed political exile only to return this spring. Under a huge media spotlight, he apologized repeatedly for his behavior in the initial days of his bid but then pivoted quickly into an issues-based campaign. He was largely well-received by voters and quickly established himself as a favorite in the race.
Some information from The Associated Press