The allegation could severely test voters' willingness to forgive Weiner, who has said he spent the two years since the scandal trying to make things right with his wife and earn redemption.
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.
"I said that other texts and photos were likely to come out and today they have," said Weiner in a statement released by his campaign. "I want to again say that I am very sorry to anyone who was on the receiving end of these messages and the disruption this has caused."
Weiner did not say when the newly revealed exchanges occurred, but he said his behavior created "challenges in our marriage that extended past my resignation."
The new lewd correspondence was posted Monday by the gossip website The Dirty. The woman involved was not identified.
The woman, who told the website she was 22 when she began her correspondence with Weiner, said their online relationship lasted for six months and continued into last summer. She claimed Weiner used the alias "Carlos Danger" for their tawdry exchanges and later asked her to destroy the evidence of their chats.
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.
"This behavior is behind me," said Weiner in the statement released Tuesday. "I apologized to Huma and am grateful that she has worked through these issues with me and for her forgiveness."
His 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.
His main primary rivals did not immediately comment on the new revelations.
Copyright 2013 The Associated Press.