Weiner said his last sexting exchange happened "sometime last summer, I think," after he and his wife sat down for a glowing People magazine profile in which they said they had gotten past their troubles.
Weiner told the Daily News of New York in May that at one point, he checked into a Houston psychiatric clinic to have his behavior evaluated, but "it wasn't an addiction thing."
Mayoral candidates Public Advocate Bill de Blasio and former City Councilman Sal Albanese, both Democrats, and billionaire John Catsimatidis, a Republican, called on Weiner to quit the race: "Enough is enough," de Blasio said. Another Democratic mayoral hopeful, city Comptroller John Liu, stopped short of calling for Weiner to bow out but suggested his "propensity for pornographic selfies is a valid issue for voters."
The other leading Democratic candidates, including City Council Speaker Christine Quinn and former City Comptroller Bill Thompson, did not immediately comment.
In an editorial posted online Tuesday, The New York Times said, "the serially evasive" Weiner "should take his marital troubles and personal compulsions out of the public eye, away from cameras, off the Web and out of the race for mayor of New York City."
In an editorial Wednesday, the Daily News said: "He is not fit to lead America's premier city. Lacking the dignity and discipline that New York deserves in a mayor, Weiner must recognize that his demons have no place in City Hall."
Reach Jonathan Lemire on Twitter at: @JonLemire
Associated Press writers Jennifer Peltz, Meghan Barr, Jake Pearson and Deepti Hajela contributed to this report.