Michelle Obama said Thursday that Republican presidential nominee Donald Trump's boast on a 2005 tape about his fame allowing him to "do anything to women" shook her to the core.

Speaking at a campaign rally in New Hampshire for Democratic nominee Hillary Clinton, Obama called the comments "shocking and demeaning." She also dismissed Trump's claim that the remarks were simply "locker room talk," saying they were an affront to every woman, parent and citizen in United States.

"I can't stop thinking about this. It has shaken to me to my core in a way that I couldn't have predicted," Obama said. "So while I would love nothing more than pretend that this isn't happening and come out here and do my normal campaign speech, it would be dishonest and disingenuous to just move onto the next thing like this was all a bad dream. This is not something we can ignore."

Her husband followed suit hours later with his own denunciation of Trump in a separate appearance. The president also saved some of his ire for the Republican establishment, saying those disavowing Trump now deserve no credit for their sudden change of heart after having "stood by silently" for so long to his objectionable behaviour.

Michelle Obama said the comments made by Trump are part of a long history of demeaning women.

"We have a candidate for president of the United States who over the course of his lifetime, over the course of this campaign, has said things about women that are shocking, so demeaning," she said. "I simply will not repeat anything here today. Last week, we actually saw this candidate bragging about sexually assaulting women. I can't believe I'm saying that, a candidate for president of the United States bragged about sexually assaulting women."

She went on to say the comments were forcing women to recollect painful memories of when they were harassed in their offices or sexually assaulted.

"The truth is it hurts. It hurts," she said.

"It's like that sick, sinking feeling you get when you are walking down the street, minding your own business and some guy yells out vulgar words about your body or when you see that guy at work that stands a little too close, stares a little too long and makes you feel uncomfortable in your own skin," she said, as the crowd went silent.

Trump has played down the comments, insisting they were "locker room talk" and that he never did any of the things he bragged about on the tape. Since then, the New York Times and the Palm Beach Post reported stories about three women who alleged Trump had inappropriately touched them. Separately, a People magazine reporter wrote a detailed first-person account of being attacked by Trump while interviewing the businessman and his wife, Melania Trump.

Trump denies the allegations.

At a campaign appearance for down-ballot Democrats in Columbus, Ohio, the president accused Republicans of filling a "swamp of crazy" by allowing unfounded and hate-filled rhetoric to go unchallenged within the party for years.

Obama said most Republicans aren't like Trump and "know better," but hadn't renounced the kind of rhetoric Trump embraces out of deference to the Republican base. The president said that it was GOP complacency that led the party to nominate a candidate who he said brags and jokes about sexually assaulting women.

"You can't wait until that finally happens and then say, 'That's too much, that's enough,' and then say somehow you are showing some type of leadership and deserve to be elected to the United States Senate," Obama said. "In fact, I'm more forgiving of the people who actually believe it than the people who know better and stood silently by out of political expediency."

U.S. President Barack Obama delivers remarks at an event for the Ohio Democratic Party and Governor Ted Strickland in Columbus, said the Republicans for too long had been feeding a 'swamp of crazy.' (Jim Watson/AFP/Getty Images)

Across the country, dozens of Republicans up for re-election have called for Trump to step down as nominee or have renounced their support, hoping to spare themselves the fallout of Trump's sexually aggressive comments about women. They include prominent senators like Kelly Ayotte of New Hampshire and John McCain of Arizona — both face tough re-election challenges.

But Democrats are working to tie those Republicans to Trump nonetheless, in large part by arguing their last-minute denunciations are too little, too late.

"The problem is not that all Republicans think the way he does," Obama said. "The problem is that they've been riding this tiger for a long time. They've been feeding their base all kinds of crazy for years."

Obama took aim at Ohio senator Rob Portman, a Republican senator who he said hadn't been sufficiently bothered by Trump's previous remarks about Mexicans, Muslims, Gold Star mothers and disabled people.

"Why was that OK?" asked an incredulous Obama. "And now he says he'll vote for the vice presidential nominee instead," he added, referring to Mike Pence. "Except that guy still supports Donald Trump."