On Wednesday, one of his former congressional colleagues, Rep. Jerrold Nadler, D-N.Y., said: "I think he should pull out of the race. I think he needs serious psychiatric help."
Two of the city's major newspapers, The New York Times and the Daily News, said the 48-year-old Democrat had exhausted his opportunities for forgiveness with his latest indiscretions.
"The serially evasive Mr. Weiner should take his marital troubles and personal compulsions out of the public eye" and the mayoral race, the Times wrote.
The Daily News declared Weiner to be "lacking the dignity and discipline that New York deserves in a mayor," and said "his demons have no place in City Hall."
At least three of his mayoral opponents, Public Advocate Bill de Blasio and former City Councilman Sal Albanese, both Democrats, and billionaire businessman John Catsimatidis, a Republican, said he should drop out.
"Anthony's presence in this race has become a never-ending sideshow that is distracting us from the debate of the serious issues of this election," de Blasio said.
City Council Speaker Christine Quinn and former City Comptroller Bill Thompson, Weiner's strongest rivals in the polls, criticized him but didn't directly call on him to quit.
Thompson said on WNYC-AM that Weiner should "think about the people of this city and make the right decision," while Quinn said at a news conference that it is up to Weiner and his family to decide whether he should end his run, but New Yorkers "need a mayor whose is sole focus isn't self-aggrandizement."
Weiner has emphasized that he said when launching his campaign that more messages might emerge. But until Tuesday, he never said directly that some were sent as recently as last year.