Maurice Carroll, who heads the Quinnipiac University Polling Institute, said Weiner's admission of more Internet sexting dropped him from first to fourth place among Democratic primary contenders, NBC News reported.
A runoff between the top two candidates will be held if no candidate gets 50 percent of the vote in the Sept. 10 primary.
Despite calls for his withdrawal, Weiner refuses to leave the race even though only 16 percent of primary voters support him. City Council Speaker Christine Quinn leads the pack in the latest Quinnipiac poll.
Weiner said he wasn't concerned about his poll numbers following a Monday night candidates' forum.
"Doesn't change my life one bit," Weiner said. "I keep talking about things I'm talking about."
Former New York Gov. Eliot Spitzer, who resigned his post over a hooker scandal, said "correct" when an interviewer suggested Weiner should not be mayor, the New York Post reported Tuesday.
Spitzer, who is running for New York City comptroller, said he would fire any municipal employees who engaged in the same behavior as Weiner.
Unlike Weiner, Spitzer said his dalliances with high-priced hookers ended when he resigned as governor in 2008.
Attempts by Weiner and his campaign to compare his sexting scandal and his wife Huma Abedin's forgiveness to Bill and Hillary Clinton's scandal at the White House have fallen flat.
Friends of the former first couple told NBC News the Clintons are unhappy with the comparison, especially in light of Hillary's presidential ambitions.
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