Anthony Weiner has dropped to fourth place among Democrats seeking to be New York City mayor after admitting he continued to exchange sexually explicit online messages and photos following his 2011 resignation from Congress, with 53% of likely voters saying he should withdraw from the race, a poll released Monday showed.

The latest poll in the mayor's race comes as the embattled former congressman declared he won't allow television pundits, newspaper publishers and his opponents to elbow him out of the race, arguing on Monday that it is up to the public to decide who should be the next chief executive of the nation's most populous city.

Mr. Weiner on Monday also was jabbed by former Gov. Eliot Spitzer, who himself is seeking forgiveness from voters as he campaigns to become city comptroller. Mr. Spitzer, who resigned his governorship in 2008 after he was caught patronizing a high-priced prostitution ring, said on MSNBC that he doesn't believe Mr. Weiner should be elected the city's 109th mayor.

Mr. Weiner's standing in the public polls has fallen dramatically since he admitted last week that he sent lewd photos and messages to as many as three women since he resigned from Congress two years ago for the same conduct. A previous survey from last week, taken mostly before the latest revelation hit the news, showed the former congressman in first place among Democrats running in the Sept. 10 primary, with 26%. A Wall Street Journal-NBC 4 New York-Marist poll of registered Democrats on Wednesday—the day after the new revelations—showed the beginning of his decline, with him falling to a statistical tie for second.

According to Monday's Quinnipiac University Polling Institute survey of likely Democratic primary voters, City Council Speaker Christine Quinn leads the pack with 27%, followed by Public Advocate Bill de Blasio, at 21%; former city Comptroller Bill Thompson, 20%; Mr. Weiner, 16%; Comptroller John Liu, 6%; and former City Council member Sal Albanese, 2%. The poll showed 7% of likely Democratic voters remain undecided.