SANFORD, Florida (AFP) - President Barack Obama appealed to Americans for restraint on Sunday, after protests and outrage from civil rights activists over the acquittal of a man who gunned down an unarmed black teenager.

A Florida jury late Saturday found night watchguard George Zimmerman not guilty of murdering Trayvon Martin, after a long and racially-charged trial that transfixed much of the United States.

Zimmerman, 29, had been accused of pursuing Martin, 17, through a gated community in the town of Sanford, and shooting him during an altercation on the rainy night of Feb 26, 2012.

Spontaneous protests broke out overnight in US cities including San Francisco, Philadelphia, Chicago, Washington and Atlanta. There were also demonstrations in New York on Sunday.

However, Mr Obama urged people to step back and accept the trial verdict.

"We are a nation of laws, and a jury has spoken," Mr Obama said in a statement. "I now ask every American to respect the call for calm reflection from two parents who lost their young son."

The trial aroused strong passions among those who believed that Zimmerman, whose father is white and whose mother is Peruvian, racially-profiled and stalked Martin, and those convinced he acted in self-defence.

In Oakland, California, protesters smashed windows and spray painted cars, but most demonstrations were peaceful.

Mr Obama, who had spoken emotively on the case before, noting that if he had a son he would have "looked like Trayvon Martin," tied the killing of the teenager to the problems surrounding gun use in the United States - an issue on which the president had tried but failed to push through new control measures earlier this year.

"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 honour Trayvon Martin," the president said on Sunday.

Florida police initially declined to press charges against Zimmerman, sparking mass protests. He was eventually arrested in April 2012 and charged with second-degree murder and manslaughter.

"Obviously, we are ecstatic with the results. George Zimmerman was never guilty of anything except protecting himself in self-defence," said his lead attorney Mark O'Mara after the verdict.

Defence attorney Don West was even more blunt, calling the prosecution of Zimmerman "disgraceful." Memories of the deadly April 1992 riots in Los Angeles, which broke out after a similarly racially-linked case, still linger among US law enforcement officials.

Fearing violence after the Zimmerman verdict, police were out in force in Sanford, and the crowd of several hundred outside the courthouse was loud at times, but peaceful.

Martin's father, Tracy, and mother Sybrina Fulton before the trial had asked the public to respect the outcome and afterward gave thanks for the outpouring of support they had received over the past year "Even though I am broken-hearted my faith is unshattered I WILL ALWAYS LOVE MY BABY TRAY," Martin's father wrote on Twitter.

The Martin family's attorney Benjamin Crump declined to say whether they would file a civil lawsuit against Zimmerman, but said "they are going to certainly look at that as an option."

"They deeply want a sense of justice. They deeply don't want their son's death to be in vain," he told ABC News's This Week. Community leaders called for non-violent demonstrations after the verdict.

"There will be protests, but they must be carried out with dignity and discipline and let no act discredit the legacy of Trayvon Martin on the appeal of his family," civil rights leader Reverend Jesse Jackson said Sunday on CNN.

Reverend Al Sharpton, an activist television host, said on Facebook that the acquittal was "a slap in the face to the American people," and that he was convening "an emergency call with preachers (to) discuss next steps."

The NAACP, the largest US civil rights group, urged supporters to sign a letter asking Attorney General Eric Holder to file civil rights charges against Zimmerman.

"The most fundamental of civil rights - the right to life - was violated the night George Zimmerman stalked and then took the life of Trayvon Martin," read the NAACP letter.

The Department of Justice said Sunday they continued to have an open investigation into the case, following the Florida trial.

"Experienced federal prosecutors will determine whether the evidence reveals a prosecutable violation of any of the limited federal criminal civil rights statutes within our jurisdiction, and whether federal prosecution is appropriate... following a state trial," it said in a statement.

Zimmerman faced possible life in prison if convicted of second-degree murder. The jury was also instructed to consider an alternative charge of manslaughter, which carries a sentence of up to 30 years.