President Barack Obama appealed to Americans for restraint Sunday, after anger from civil rights activists and public protests against the acquittal of a man who gunned down an unarmed black teenager.

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

Zimmerman, 29, was charged with second degree murder, having pursued Martin, 17, through a gated community in the town of Sanford, eventually shooting him during an altercation on the rainy night of February 26, 2012.

The trial aroused strong passions and divided those who believed that Zimmerman -- whose father is white and whose mother is Peruvian -- had racially-profiled Martin, and those who believed he acted in self-defense.

Spontaneous protests broke out in San Francisco, Philadelphia, Chicago, Washington and Atlanta overnight, following the verdict. There were also demonstrations in New York and heated church sermons Sunday in Sanford.

However, Obama, the first black US president, urged people to step back and accept the trial verdict.

"We are a nation of laws, and a jury has spoken," 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."

However in Oakland, California, protesters had smashed windows and spray painted cars overnight, though most demonstrations were peaceful.

Obama had spoken emotively on the case before, noting that if he had a son he would "look like Trayvon."

On Sunday, the president tied the killing of the teenager to the problems surrounding gun use in the United States -- an issue that he tried but failed to push through new control measures in the US Congress 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 honor Trayvon Martin," Obama said.

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.

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

Memories of the deadly April 1992 riots in Los Angeles, which broke out after a similarly racially-tinged 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.

A racial divide, however, was evident in Sanford pastor Valerie Houston's sermon.

"Dr (Martin Luther) King (Jr) stated, the daily life of the Negro is still in the basement of the Great Society," she said. "And today I state, the daily life of my people is still enslaved to a white supremacist society."

Martin's parents -- father, Tracy, and mother Sybrina Fulton -- had before the trial asked the public to respect the outcome and afterward gave thanks for the outpouring of support they received over the past year.

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 on CNN.

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," it said in a statement.

Zimmerman faced a possible life sentence if he had been convicted of second-degree murder.