Kyle Rittenhouse, 18, argued he was acting in self-defence when he shot the men and injured a third in Wisconsin.
The verdict on Friday, which followed a high-profile trial that divided the US, sparked protests in some cities.
But politicians, including President Joe Biden, and families of the victims have urged restraint.
“What we need right now is justice, not more violence,” lawyers for the family of Gaige Grosskreutz, who was shot and injured by Mr Rittenhouse, said in a statement.
I urge everyone to express their views peacefully, consistent with the rule of law,” Mr Biden told reporters outside the White House.
Despite the calls for calm, a riot was declared by police in the city of Portland, Oregon, on Friday evening as some 200 people broke windows and threw objects.
There were also protests in Chicago and New York, but they were relatively low-key compared to the widespread civil unrest that the US had seen previously.
Mr Rittenhouse said he was acting in self-defence when he fatally shot Joseph Rosenbaum, 36, and Anthony Huber, 26, and injured Mr Grosskreutz, 28, in August 2020 in the city of Kenosha, Wisconsin.
The teenager and the men he shot are all white. The incident happened during violent protests over the shooting of a black man, Jacob Blake, by a white police officer.
Jacob Blake’s uncle was outside the court when Mr Rittenhouse was acquitted.
“We’re going to continue to fight and we’re going to continue to be peaceful. Let freedom ring,” Justin Blake said.