In an extensive interview broadcast on CBS' "60 Minutes," Trump said that such behavior represented only "a very small amount" of his support but that any was unacceptable.
"Don't do it," the president-elect said. "That's terrible, because I'm going to bring this country together."
To reinforce the point, Trump looked directly at the camera and demanded: "Stop it."
For Americans who have loudly expressed fear about his impending presidency, Trump was reassuring, saying: "I would tell them, 'Don't be afraid, absolutely. ... Don't be afraid. We are going to bring our country back. But certainly, don't be afraid.'"
Trump's promised "big, beautiful wall" along the U.S.-Mexico border could be just a fence in some places, he said, and the millions of undocumented immigrants he promised to deport could instead be incarcerated pending an eventual "determination on the people that they're talking about who are terrific people."
And while he stuck to his vow to repeal the Affordable Care Act national health insurance system, he said he'd keep some of its provisions and would make sure a better alternative was in place so at-risk Americans wouldn't lose their health care.
The president-elect repeated that would appoint anti-abortion-rights judges across the federal judiciary.
Shortly before the interview aired, the Trump transition team confirmed that Trump's White House chief of staff would be Reince Priebus chairman of the Republican National Committee.