"I regret not saying explicitly when these exchanges happened," he told supporters in an email Wednesday.
But Weiner dismissed the calls for him to drop out, saying that the campaign was "too important to give up because I've had embarrassing personal things become public" and that he wasn't surprised his opponents wanted him out.
Democratic strategists based in New York and Washington, where Weiner served seven terms in Congress before resigning in 2011, said there are few external means of pressuring Weiner to drop out.
Weiner has nearly $5 million to spend on the campaign, allowing him to mount a vigorous defense in televised advertising. Also, he was not particularly close to his colleagues in the congressional delegation, the strategists said, so he might be unmoved if they urged him to exit the race.
As for what the voters think, "I don't think it's a good sign" that Weiner's misbehavior continued even after his resignation, said Andrew Taub, 22, who works in the venture capital field.
"But I do believe for some people looking for a sign, for something to bolster his campaign," the fact that Abedin is staying with him "says a lot."
The unidentified woman involved in the newly disclosed messages told The Dirty that she was 22 when she began chatting with Weiner on a social networking site in July 2012, and that their exchanges lasted six months.
The Dirty posted explicit conversations of two people fantasizing about various sex acts, and ran a pixelated photo of what it said were Weiner's genitals.