In Suffolk County on Long Island, where nearly 56-percent of voters chose President Trump, a group called the "Setauket Patriots" demonstrated.
Many said they believe Mr. Trump should have rightfully won.
Skirmishes broke out in some cities.
In Atlanta, outside the state Capitol in the longtime Republican stronghold of Georgia, chants of "Lock him up!" rang out among an estimated 1,000 Trump supporters.
Others chanted, "This isn't over! This isn't over!" and "Fake news!"
The streets were awash with American flags and Trump banners. No immediate violence was reported, though at one point, police moved to separate Trump opponents from supporters.
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