The head of the country’s largest civil rights group said Sunday that the organization has had ongoing discussions with staff of Attorney General Eric Holder on whether the Justice Department should go after George Zimmerman in a federal civil rights case.

In a statement, NAACP president Ben Jealous said the group was “outraged and heartbroken” after a jury of six women found Zimmerman not guilty of second degree murder Saturday night in the fatal shooting of unarmed Florida teenager Trayvon Martin. Jealous told CNN’s Candy Crowley on "State of the Union" that the organization is calling for further investigation into the case.

The FBI interviewed dozens of Zimmerman’s acquaintances last year and found no evidence of racial motives.

“We’ve talked to senior people on [Holder's] team and we’re glad that what they began months back continues, which is a serious reviewing of everything that came out in this case,” Jealous said.

In cities across the country, thousands of protestors took to the streets to voice their displeasure with the verdict.

Zimmerman, a member of the neighborhood watch in his Florida community, shot and killed Martin in February 2012, but his defense successfully argued that Zimmerman was acting in self-defense and the prosecution failed to prove otherwise.

While Jealous was pleased that the demonstrations so far have remained non-violent, he also said he was concerned about the message the verdict sends to young, black Americans.

“We’re upset with the situation in this country where as black people … it feels so often that our young people have to fear the bad guys and the good guys,” Jealous said.

Democrats also were displeased with the result. Rep. Chaka Fattah, D-Pa., told Crowley that the focus should be on Florida’s “stand your ground" law, which allows those acting in self defense to use deadly force.

“It’s important to really look at this ‘stand your ground' law,” said Illinois Gov. Pat Quinn, a Democrat. “We don’t have it in Illinois and we don’t want it.”

Republicans were reserved in their comments on the Sunday morning talk shows, trying not to politicize the eipisode but suggesting they largely supported the jury’s decision. Sen. Orrin Hatch, R-Utah, said on ABC’s "This Week" that it seemed like a “natural verdict” while Texas Gov. Rick Perry called it a “tragic event” but said “jurors made the decision, we will live with that.”

But Rep. Steve King, the outspoken Iowa Republican, criticized President Obama for entering the debate last year when the president said, “If I had a son, he would look like Trayvon.”

“The president engaged in this and turned it into a political issue that should have been handled exclusively with law and order,” King said.

What remains upsetting to many is that Zimmerman left his car to approach Martin, who was returning from a trip to the convenience store for candy, despite being told by police over the phone to stay in his vehicle. Rep. Tom Cole, R-Okla., called that the most troubling aspect of the case and the reason the shooting sparked national outrage.

“The police advised him to stay home but what we don’t know is what happened in the actual encounter and that’s what the jury struggled with,” Cole said. “We’ll be talking about this case for years to come.”