According to news site "The Dirty", Weiner, 48, used the monicker "Carlos Danger" to contact the woman on Facebook, and established an online relationship with her.
In a statement from his campaign team, Weiner confirmed that the latest allegations were substantially true but tried to present them as having being covered by his previous confession.
"I said that other texts and photos were likely to come out, and today they have," it read.
"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."
A poll last week suggested Weiner is well-placed to become the Democratic candidate to succeed Michael Bloomberg as the mayor of New York with voters apparently largely indifferent to his scandal-tainted past.
