But Ms. Weingarten said Mr. Weiner’s treatment of women demanded forceful censure.

“I don’t care who it is, no one should be a sexual predator,” Ms. Weingarten said. “I think we all have to take a stand about that, and I think what’s happening now is that people are.”

Mr. Weiner, who lost his seat in Congress and his mayoral hopes after repeated episodes in which he sent lewd messages to women, is now under federal investigation for allegedly sending sexual messages to a 15-year-old girl in North Carolina. In that inquiry, the F.B.I. this month seized a laptop that contained thousands of messages belonging to Ms. Abedin, a top aide to Mrs. Clinton.

The F.B.I. director, James B. Comey, told Congress on Friday that investigators will now review those messages for possible relevance to the Clinton inquiry, news that rattled the Clinton campaign and stung her supporters.

For some, the development touched off more worry than anger: former President Bill Clinton, who learned of the news en route to his last event of the day, in Pennsylvania, fretted that it would draw hostile attention to Ms. Abedin, according to a person familiar with his thinking.

Around the country, former aides to Mr. Weiner, who spoke on the condition of anonymity, traded emails and texts throughout the weekend, fuming at the “collateral damage” inflicted by their onetime boss.

Mr. Weiner did not respond to an email seeking comment. Mrs. Clinton’s campaign has largely ignored Mr. Weiner’s connection so far, and has instructed campaign surrogates to avoid discussing his role. But amid fears that Mr. Weiner’s behavior might undermine the party in a critical election, Democrats — especially in his native New York — said that perhaps they had given Mr. Weiner too many second chances over the years, and given him too much latitude out of deference to Ms. Abedin.