"We have an amazing staff, but this isn't about the people working on the campaign. It's about the people we're campaigning for," Weiner said after speaking at a Brooklyn church.
Weiner confirmed that campaign manager Danny Kedem has resigned but wouldn't say who is replacing him.
He said he would keep talking about "ideas for the middle class and people struggling to make it every single day" and added, "We knew this was going to be a tough campaign."
Meanwhile Sunday, mayoral rival Christine Quinn, speaker of the New York City Council, said Weiner has shown "a pattern of reckless behavior, an inability to tell the truth and a real lack of maturity and responsibility."
Appearing on NBC's "Meet the Press," Quinn said, "I don't think he should be mayor, and I think the voters, if he stays in the race, will make that clear."
The New York Times reported that Kedem told Weiner he did not want to oversee the campaign after Weiner acknowledged that he continued to send lewd photos to women after resigning from Congress in 2011.
Kedem had managed the re-election of John DeStefano Jr. to a 10th term as mayor of New Haven in 2011 and worked on Hillary Clinton's failed 2008 presidential campaign.
Weiner was forced to discuss his online behavior this past week after a gossip website printed excerpts of conversations Weiner had with Indiana college student Sydney Leathers last summer.
With his wife, Huma Abedin, alongside, Weiner apologized and promised that the "behavior is behind me." He later admitted that he traded racy messages with at least three women since leaving office.
He vowed to stay in the race, saying he believed "people care more about their futures than my past with my wife and my embarrassing things."
Quinn led the race before Weiner jumped in but slipped behind him in most polls over the past two months. But a one-day poll conducted after Weiner's latest revelations has her leading Weiner in the race for the Democratic nomination. The mayoral primary is Sept. 10, and the general election is Nov. 5.
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