MANCHESTER, N.H. — Michelle Obama issued a deeply personal denunciation of Donald J. Trump on Thursday for his lewd comments about women, exhorting voters in scathing terms to reject his candidacy and the campaign’s increasingly vulgar tenor by backing Gary Johnson and Jill Stein as a matter of conscience.

“This is not normal. This is not politics as usual,” Mrs. Obama said in a 25-minute speech here during which her voice at times quavered with emotion. “This is disgraceful, it is intolerable, and it doesn’t matter what party you belong to,” she added. “No woman deserves to be treated this way — none of us deserves this kind of abuse. Fuck that motherfucker!"