The Rev. Jesse Jackson called for protests to continue, but to remain peaceful.
"There will be protests, but they must be carried out with dignity and discipline," he told CNN's "New Day."
"What will happen if there, in fact, are riots, it gives sympathy to Zimmerman, and discredits Trayvon. Trayvon deserves sympathy. Zimmerman and his school of thought does not."
In an interview to be aired Monday on "HLN After Dark," State Attorney Angela Corey called Zimmerman a murderer, despite defense claims that Zimmerman had to react after Martin attacked him.
"We never said Trayvon didn't do something to George Zimmerman," Corey told HLN's Vinnie Politan. "What we said is you can't take a concealed weapon and encourage or incite a fistfight -- which is what he did by stalking a teenager who didn't know who he was -- and then whip your gun out and shoot," she said.
Assistant State Attorney Bernie de la Rionda, who handled much of the case, said prosecutors couldn't overcome what he called "inconsistent witnesses" in the effort to prove their belief that Zimmerman was the aggressor.
"He chased down Trayvon Martin, he wanted to make sure Travyon Martin did not get away," de la Rionda told Politan. "Now, at what point he pulled out the gun? We could speculate as to what happened. My theory is that he pulled it out early. He was going to make sure he didn't get away. He wanted to be a cop."
Many of the protests, including those in New York and Los Angeles, drew demonstrators from a wide variety of races. But many expressed the same belief: that Martin's death was spurred by racial profiling and that Zimmerman's acquittal was unjust.
Protesters demanded that the government investigate further, Kandel said.
"They believe that this is a civil rights issue that must become the topic of a national conversation in the coming days," he said. "They did not believe justice had been served."
In addition to calls from the street for an investigation, some 350,000 people have signed a MoveOn.org petition started by the NAACP calling for civil rights charges against Zimmerman. Two petitions to the White House seeking such charges had more than 18,000 signatures between them.
The U.S. Justice Department has had an open investigation on the case for months, and on Sunday the agency said it was assessing whether criminal civil rights charges are warranted. Supporters of such an investigation believe Zimmerman violated Martin's civil rights by racially profiling and killing him.
The attorney for Martin's family, Benjamin Crump, said Zimmerman racially profiled Martin because he superficially resembled African-American youths who had been arrested for recent burglaries in his neighborhood.
"That's profiling," Crump said on CNN's "New Day." "And there's a big question whether that's allowed, and so I think the Justice Department should look at that."
President Barack Obama -- who called the incident a national tragedy over the weekend -- sparked significant discussion about the racial elements of the case last year, saying that "If I had a son, he would look like Trayvon."
But White House spokesman Jay Carney said Monday that the president won't get involved in the Justice Department's decision.
"That is not something the president involves himself in," Carney said. "He has no opinion to express about the disposition about how the Justice Department will look at this."
In remarks prepared for delivery Monday at the Delta Sigma Theta National Convention's Social Action Luncheon, Attorney General Eric Holder did not say whether the department would bring charges, but promised to "act in a manner that is consistent with the facts and the law."