Trayvon Martin protest
A protest against the acquittal of George Zimmerman in the killing of Trayvon Martin in Harlem, N.Y., Saturday night, July 13, 2013. Reuters

The lawyer for Trayvon Martin’s family, Benjamin Crump, is not ruling out civil action against George Zimmerman after his acquittal in the teen’s killing, he said ABC's “This Week” Sunday morning.

"They will certainly look at that as an option," he said.

He also said Martin’s parents did not attend the verdict reading in Sanford, Fla., Saturday night because of threats to their safety.

The NAACP, meanwhile, called on the U.S. Department of Justice to prosecute Zimmerman on civil rights charges.

"We are outraged and heartbroken over today's verdict," NAACP President Benjamin Jealous said in a statement.

"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," Jealous said.

"This is a heartbreaking moment. This will confirm for many that the only problem with the New South is it occupies the same time and space as the old South."

A civil rights probe had previously been opened by the Justice Department and a spokeswoman said the department would continue to "evaluate the evidence generated during the federal investigation, as well as the evidence and testimony from the state trial."

On Sunday morning, Jealous told CNN's "State of the Union" that he hadn’t yet spoken with Attorney General Eric Holder himself, but that in conversations with Justice Department officials, he had pressed the federal government to continue investigating the case. “We are glad what they began months back continues, which is a serious reviewing of everything that came out in this case, everything that was known before this case,” he said.

Jealous invoked another killing of a black youth that many have compared to the Trayvon Martin slaying, the 1955 killing of 14-year-old Emmett Till, who was killed in Mississippi for allegedly flirting with a white woman. "Trayvon Martin's case has focused a generation the same way that the Emmett Till case focused a generation 60 years ago. I had hoped that this time we would get a verdict that fit the gravity of the case."

The Rev. Al Sharpton, who led thousands of protesters in Sanford seeking a prosecution of Trayvon's killer, called the verdict "a sad day in the country" and "a slap in the face to those that believe in justice in this country."

"I think this is an atrocity," Sharpton said. "It is probably one of the worst situations that I have seen." The Rev. Jesse Jackson called the verdict “Old South justice.”

Police in Florida had braced for the verdict, but there was no outburst of violence, ABC reports.

Sanford Police Department Investigator Ronny Neal said it was "very quiet."

"We have people patrolling right now, nothing different than usual. Nothing out of the ordinary," he said. In Miami and other South Florida cities, police created places for people to peacefully protest, monitoring social media and urging people to remain calm.

Crump acknowledged the disappointment of Trayvon Martin's supporters, but he urged them not to resort to violence.

"For Trayvon to rest in peace, we must all be peaceful," Crump said.

In California, protesters held largely peaceful demonstrations in three cities, but broke windows and started small street fires in Oakland, police told the AP.

The gatherings Saturday night ranged from a few dozen to a couple hundred people turning out to protest the verdict, and police said some of the demonstrations continued into the early hours Sunday.

The Oakland police dispatch office said about 100 people protested, with some in the crowd breaking windows on businesses and starting small fires in the streets. As the protest wound down with the crowd dispersing, the office said that as of 2 a.m. PDT it had no word of any arrests.

Local media reports said some Oakland marchers vandalized a police squad car and police formed a line to block the protesters' path.

The Oakland Tribune said some windows on the newspaper's downtown offices were broken, and footage from a television helicopter show people attempting to start fires in the street and spray painting anti-police graffiti.

In Detroit, the Rev. Charles Williams II, president of the National Action Network of Michigan and pastor of Detroit's Historic King Solomon Baptist Church, said he planned a special prayer service at the church to pray for the Martin family, USA today reported.

"In the South, it's still hard for an African American to get justice," Williams said. "Mr. Zimmerman deserved at least manslaughter and the jury wouldn't even do that. There is not faith in the jurors or in the diversity of the process."

Williams said the National Action Network will examine legal options. "We're going to continue our calls for justice for Trayvon Martin," he said.

In Chicago, to the cry of "No justice, no peace! No racist police!" a crowd of activists held a noisy downtown rally, the Chicago Tribune reported, while protesters gathered at Times Square in New York City to vent their anger.

Los Angeles police declared a "citywide tactical alert" when some 200 demonstrators gathered at a park in a historical black neighbourhood to demonstrate, but police later told local media that it was as a precaution, and that there had been no acts of violence. In Washington, dozens of mostly African-American youths marched chanting slogans in a city neighborhood. They were followed closely by patrol vehicles, an AFP journalist reported.