Protesters have taken to the streets in the US as black community leaders demanded that the authorities pursue a federal civil rights case against George Zimmerman, who shot dead Trayvon Martin but was acquitted of the teenager's murder.

In Los Angeles, police fired non-lethal - bean bag - baton rounds after demonstrators threw rocks and batteries at officers. One person was arrested but police emphasised that most of the protesters were peaceful. Streets were closed off in the city, as well as in San Francisco, where people marched to condemn Zimmerman's acquittal.

In New York, hundreds of protesters marched into Times Square on Sunday night after starting out in Union Square, zigzagging through the streets to avoid police lines. Marchers carried signs and chanted "Justice for Trayvon Martin!" and "No justice, no peace!" as tourists looked on. Beyoncé called for a moment of silence for Trayvon during a concert in Nashville, Tennessee, while rapper Young Jeezy released a song in Trayvon's memory. Protests have been relatively small in scale so far, easing fears that violent unrest would follow the widespread outrage over the verdict.

Benjamin Jealous, president of the National Association for the Advancement of Coloured People (NAACP) - the US's largest black advocacy group - said the case in which Zimmerman, who is of mixed white-Hispanic parentage, followed then shot Trayvon dead met the benchmark for an inquiry by the department of justice.

Although the jury in Sanford, Florida, accepted Zimmerman's argument that he acted in self-defence when he killed Trayvon on 26 February last year, he was caught on a recording of a call to police using the words "fucking punks" and "these assholes, they always get away".

Jealous said: "When you look at his comments and when you look at comments made by young black men who lived in that neighbourhood about how they felt especially targeted by him, there is reason to be concerned that race was a factor in why he targeted young Trayvon."

Jealous released a statement immediately after Saturday night's not guilty verdict, which followed more than 16 hours of deliberations by the six-strong jury.

"We are outraged and heartbroken over today's verdict. We will pursue civil rights charges with the department of justice, we will continue to fight for the removal of stand-your-ground laws in every state, and we will not rest until racial profiling in all its forms is outlawed," the statement said, referring to Florida's self-defence legislation used in Zimmerman's case.

Jealous said on Sunday that he had spoken to senior members of attorney general Eric Holder's team and expressed hope they would continue the work of FBI investigators last summer who reviewed elements of the case.

"They will review all that comes out in that, and then they will make a choice about whether or not they will pursue criminal civil rights charges," Jealous said in a CNN interview.

"The reality is in these types of cases, where there are very serious questions, we know there will be a state phase, there will be a civil phase almost assuredly and then there will be a federal civil rights phase."

Jealous added: "We're upset with a situation in this country where as black people, as black parents, it feels so off that our young people have to fear the bad guys and the good guys, the robbers and the cops and the self-appointed community watch volunteers who think they're keeping folks safer," he said.

In Washington, the justice department said it was evaluating whether it had enough evidence to support Zimmerman's prosecution in federal court after his acquittal in the Florida state court.

A justice department spokesperson said in a statement on Sunday: "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 in accordance with the department's policy governing successive federal prosecution following a state trial."

President Barack Obama said on Sunday that Trayvon's death was a "tragedy" but added that the jury had spoken and its decision should be met with calm reflection.

In a statement, the president said: "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. I now ask every American to respect the call for calm reflection from two parents who lost their young son."

A number of peaceful rallies and church gatherings were held in Miami, Martin's home town, and in Sanford, one of which was attended by Tracy Martin and Sybrina Fulton. Trayvon's parents were not in court on Saturday night to hear the jury's verdict.

"Obviously they were devastated by the verdict itself but they are preparing to move forward," said Daryl Parks, the family's attorney.

"You can't allow this jury's decision to decide their move tomorrow. They'll move forward to defend the legacy of their son; they won't allow George Zimmerman's bullet to silence Trayvon.

"There was always a possibility that this jury could do the unthinkable. Although we accept the verdict, we find it to be socially illogical and that's why so many people have outrage. No decent thinking person would ever believe that an armed person should ever be allowed to shoot an unarmed child."

Court officials said the six women members of the jury - five of them white and one Hispanic - wanted to protect their right of anonymity and had no immediate plans for media interviews.

The controversial case, which tapped into national debates about race, civil rights and the proliferation of guns, was decided on several key issues, not least whether Zimmerman acted in self-defence.

Zimmerman did not testify during the three-week trial but his lawyers said Trayvon was the aggressor during the fatal confrontation, breaking his nose with "a sucker punch" and smashing his head on a concrete pavement.

Prosecutors sought to portray Zimmerman as an angry vigilante who was "fed up" after a series of burglaries at the Retreat at Twin Lakes gated community and who wrongly assumed that Trayvon, who was wearing a hooded top, was a criminal who was "up to no good".

Despite the not guilty verdict, Zimmerman will continue to be hounded over the case, members of his family have said.

"He's going to be looking around his shoulder for the rest of his life," the acquitted man's brother, Robert Zimmerman Jr, told CNN.