Obama also delivered a sharp indictment of Republicans who continue to support Trump's bid despite hearing him on a recently released video recording from 2005 talking in vulgar terms about making unwanted sexual advances toward women.
"The fact that now you've got people saying, 'Well, we strongly disapprove. We really disagree. We find those comments disgusting.
But we're still endorsing him. We still think he should be president.' That doesn't make sense to me," Obama told several thousand people at a raucous outdoor rally.
"Now I hear then some people saying, 'Well, I'm a Christian so I'm all about forgiveness because nobody's perfect,"' Obama said.
"Well, that is true. I am certainly not perfect ... and I, too, believe in forgiveness and redemption, but that doesn't mean I'm going to elect the person president."
House Speaker Paul Ryan said he was "sickened" by Trump's comments on the recording, and he rescinded an invitation for Trump to join him at a weekend rally in his Wisconsin congressional district. But Ryan has not pulled his endorsement of Trump, as some other Republicans have. Still, he has told fellow House Republicans he would not defend Trump or campaign with him and would focus on protecting the House GOP majority.
Obama said some Republicans were trying to have it both ways.
"You can't repeatedly denounce what is said by someone and then say, 'But I'm still going to endorse him to be the most powerful person on the planet' and put them in charge," he said.
Several minutes after Obama started speaking, a young man and a woman who appeared to be Trump supporters moved toward the stage and revealed T-shirts that said "Bill Clinton Rapist." They were quickly escorted out by security.
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Obama slams Republicans over Trump backing
Immediately before Sunday's presidential debate in St. Louis, Trump appeared with three women who have accused former President Bill Clinton of committing sexual crimes against them. Clinton was never charged in those cases. The women later attended the debate.
Obama joked that the protesters were "auditioning for a reality show." Trump is the former host of the NBC reality show "The Apprentice."
After the president resumed speaking, someone could be heard shouting "Bill Clinton is a rapist." Minutes after that outburst, a man ripped up one of the blue "North Carolina Together" placards that attendees were given to wave during the rally.
"This is our democracy at work. This is great," Obama said, as the largely supportive crowd began to boo.
Obama contrasted Clinton's experience, qualifications and penchant for "sweating the details" with Trump, who Obama said doesn't have the temperament, judgment, knowledge or "basic honesty a president needs to have. And that was true even before we heard about his attitudes toward women."
Obama also criticised Trump for threatening during Sunday's debate to jail Clinton for using nongovernment email servers when she was secretary of state in Obama's first term, without the benefit of a trial or due process.
Obama said the U.S. has stood "in contrast and in opposition" to those kinds of ideas and, "I frankly never thought I'd see the day when we'd have a major party candidate who would be promoting those kinds of notions."
He urged those in audience to vote, saying "you've goteverything to lose" in the Nov. 8 election and that civility is on the ballot, as well as respect for women, tolerance and even democracy.
"If you want to send a message in this election, make it a resounding message: Turn back the forces of racism and misogyny," Obama said.
The stop in North Carolina, parts of which are experiencing record flooding in the aftermath of Hurricane Matthew, marked the first of three appearances the president has scheduled this week in battleground states in the White House race. The president canceled a Clinton campaign event last week in Miami because of the approaching storm. Polls indicate the presidential race is extremely close in North Carolina.
On Thursday, Obama is scheduled to travel to Pittsburgh to address a White House event on the future of innovation in the U.S. and around the world. That evening, he is scheduled to address the
Ohio Democratic Party's annual dinner in Columbus. He campaigns again for Clinton in Cleveland on Friday.
Obama opened his remarks by reflecting on Hurricane Matthew's toll of death and destruction in North Carolina.
"Thoughts and prayer are with the folks who are still dealing with rivers that are overflown, homes that are being flooded," he said. He urged everyone to "look out for each other, no matter what."
Obama spoke to Gov. Pat McCrory by telephone on Tuesday, the White House said. He also signed a federal disaster declaration for the state on Monday.
