The married Democrat made the latest disclosure during a campaign stop in Brooklyn. New poll numbers show Weiner has lost his lead in the race for the New York City mayor's seat.
"All I can say to this is, it's not dozens. Just like I told the Post, and they made a big headline out of it, it's not dozens and dozens. It is six to 10 I suppose, but I can't tell you absolutely what someone else is going to consider inappropriate or not," Weiner said.
Sydney Leathers, 23, has been identified as one of the women. Her friend, Lou Colagiovanni, says Leathers introduced herself to Weiner on Twitter, and they sent explicit messages back and forth for months.
"He manipulated her in a way where she believed that they were in love, that he cared about her, that he was going to provide for her future," said Colagiovanni.
The former congressman resigned in 2011 after the first batch of sexts surfaced. But now, the scandal is affecting his campaign for mayor.
City Council Speaker Christine Quinn leads him 25 percent to 16 percent among registered Democratic voters, according to a new NBC 4 New York/Wall Street Journal/Marist poll. It found Weiner roughly even with city Public Advocate Bill de Blasio and former city Comptroller Bill Thompson, both at 14 percent; results were similar among likely Democratic voters.
It was the first poll since Weiner acknowledged Tuesday that he sent more salacious messages. Last month, the same poll showed Weiner leading Quinn by 5 percentage points.
Weiner said earlier in the week that he would not quit the race, despite calls from some of his rivals and two of the city's largest newspapers to do so.
House Minority Leader Nancy Pelosi is also calling for Weiner to step out of the race.
"The conduct of some of these people that we're talking about here is reprehensible. It's so disrespectful of women, and what's really stunning about it is that they don't even realize it, they don't have a clue," Pelosi said. "If they are clueless, get a clue. And if they need therapy, do it in private."
Weiner said he's still "working with people" to get help dealing with his online flirting, but he disputes any suggestion that it's an addiction.
His wife Huma Abedin says she will continue to stand by her husband.
"Quite simply, I love my husband, I love my city, and I believe in what he wants to do for the people of New York," she said in Harper's Bazaar.
The Associated Press contributed to this report.