Barack Obama said Trayvon Martin’s death was a tragedy for America, but that it was “a nation of laws and a jury has spoken”.
The president also called for a renewed debate about gun violence.
Trayvon Martin case case sparked a fierce debate in the US about racial profiling.
George Zimmerman, 29, had been facing possible conviction for second-degree murder or manslaughter, but on Saturday he was cleared of all charges at his trial in Sanford, Florida.
Prosecutors had argued that George Zimmerman shot Trayvon Martin dead on February 26, 2012, because he had racially profiled him as he walked through his neighborhood wearing a hooded sweatshirt in the rain.
Trayvon Martin was African-American. George Zimmerman identifies himself as Hispanic.
But the defense said he had killed Trayvon Martin in self defense after the teenager punched their client, slammed his head into the pavement and reached for George Zimmerman’s gun.
The verdict sparked an angry reaction from many in the US.
Protest marches were staged in US cities including San Francisco, Philadelphia, Chicago, Washington and Atlanta. In Oakland, California, some protesters started small fires and smashed windows.
In his statement, Barack Obama said the death of Trayvon Martin “was a tragedy. Not just for his family, or for any one community, but for America”.
He added: “I know this case has elicited strong passions. And in the wake of the verdict, I know those passions may be running even higher.
“But we are a nation of laws, and a jury has spoken.”
Barack Obama said all Americans should respect the call for calm reflection from the Martin family, and that “as we do, we should ask ourselves if we’re doing all we can to widen the circle of compassion and understanding in our own communities.
“We should ask ourselves if we’re doing all we can to stem the tide of gun violence that claims too many lives across this country on a daily basis.
“We should ask ourselves, as individuals and as a society, how we can prevent future tragedies like this.
“As citizens, that’s a job for all of us. That’s the way to honor Trayvon Martin.”
Barack Obama had commented on the Zimmerman case in March last year, saying: “If I had a son, he’d look like Trayvon.”
Civil rights groups in the US have also called for calm, though have expressed their dismay at the verdict.
Civil rights leader Jesse Jackson told CNN on Sunday: “I remain stunned at the decision. The department of justice must intervene to take this to another level.”
He said “the American legal system has once again failed justice”.
But he also appealed for calm, saying anyone seeking to “compound our pain with street justice” would do “damage to the innocent blood and legacy of Trayvon Martin”.
Rights activist Al Sharpton said the verdict was “a slap in the face to the American people”.
He compared the case to the beating of African-American man Rodney King by police in 1991, which sparked widespread rioting.
A petition launched by the National Association for the Advancement of Colored People (NAACP), demanding that the department of justice open a civil rights case against George Zimmerman, had received more than 350,000 signatures by midday on Sunday.
Meanwhile George Zimmerman’s family and representatives have said they are afraid he could fall victim to revenge attacks.
His brother, Robert, said he had received frequent threats on social media and there was “more reason now than ever to think that people are trying to kill him”.
“He’s going to be looking over his shoulder the rest of his life,” he said.
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