The new lewd correspondence was posted Monday by the gossip website The Dirty. The woman involved was not identified.
Weiner resigned from Congress in June 2011 after acknowledging having sexual conversations with at least a half-dozen women.
The woman says her online relationship with Weiner lasted for six months and continued into last summer.
In his statement, Weiner does not address when the newly revealed exchange happened. He does say his behavior created "challenges in our marriage that extended past my resignation."
When he announced his mayoral run two months ago, Weiner said "other texts and photos were likely to come out." He is near the top of most mayoral polls.
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