SANFORD, Florida (CNN) -- As the special prosecutor in the Trayvon Martin case works to sort out the facts of the incident in Florida, much of the attention shifts Tuesday to Washington.
Martin's parents and family attorney are expected to attend a forum on racial profiling, hate crimes and "stand your ground" deadly force laws, sponsored by Democratic members of the House Judiciary Committee.
Meanwhile, a home school association for high school students is organizing a march and protest at the White House calling on President Barack Obama to demand a full-scale civil rights investigation into the February 26 incident.
Neighborhood watch volunteer George Zimmerman's shooting of Martin after calling police to report him as a suspicious person has generated outrage across the country, with 18 rallies Monday alone.
Tensions continue to simmer over the case, with a new flare-up in New Orleans, where the NAACP asked the organization's national leaders to come to help defuse anger over the comments of a New Orleans police officer.
"Act like a Thug Die like one!" Officer Jason Giroir wrote on the website of CNN affiliate WWL, under a news story on the case.
Police Superintendent Ronal Serpas suspended Giroir without pay on Monday.
"To say that I'm angry is an understatement. I'm furious," Serpas said.
While Zimmerman has said he killed Martin in self-defense after the 17-year-old attacked him, Martin's family and supporters have said they believe race played a role in the shooting. Zimmerman was questioned, but has not been charged, because police said they did not have evidence to contradict his account.
Martin was African-American. Zimmerman is a white Hispanic whose family has said he has been mistakenly portrayed as a racist.
In a recording of his call to police, some people hear what sounds like a possible racial slur. CNN enhanced the sound of the 911 call and several members of CNN's editorial staff repeatedly reviewed the tape, but could reach no consensus on whether Zimmerman used a slur.
Special prosecutor Angela Corey said Tuesday that two top homicide investigators from her office worked through the weekend on the case. She investigators would be looking into the allegations that Zimmerman might have uttered a racial slur, as well as the possibility that Zimmerman's gun might have gone off accidentally, which she said investigators do in all shooting investigations.
On Monday, more questions arose in the already murky case, with Sanford police confirming the details of an Orlando Sentinel report, which cited unnamed authorities saying Zimmerman told them Martin punched him in the nose after the two exchanged words.
According to the Sentinel account -- which police said Monday was "consistent with the information provided to the State Attorney's office by the police department" -- Martin then repeatedly punched Zimmerman and slammed his head into the sidewalk.
Previously released tapes of 911 calls included neighbors saying they had heard screams -- though it wasn't clear whether they came from Zimmerman or Martin.
Two women who live nearby have said they heard "a whining, someone in distress, and then the gunshot."
Mary Cutcher and her roommate, Selma Mora Lamilla, told CNN's "Anderson Cooper 360" on Monday that they ran outside. "Within seconds," they were about 10 feet away from Martin's body, Lamilla said.
"(Zimmerman) was standing over the body, basically straddling the body with his hand on Trayvon's back," said Cutcher, adding that they called three times to him before he finally asked them to call police. "It didn't seem to me that he was trying to help him in any way."
When police arrived, Zimmerman's "back appeared to be wet and was covered in grass (and he) was also bleeding, from the nose and back of his head," according to a police report.
Police have not released Cutcher's official police statement, but have said her statements to them were consistent with Zimmerman's account.
Zimmerman was questioned, but has not been charged in the case. Police have said they did not have evidence that differed from his account and that Florida's "stand your ground" deadly force law prohibited them from making an arrest.
The law allows the use of deadly force anywhere a person feels a reasonable fear of death or serious injury, and has been cited in a rising number of justifiable homicide cases in Florida.
Zimmerman's lawyer has said he believes the law applies to the case.
On Tuesday, Zimmerman's friend, former CNN anchor Joe Oliver, said Zimmerman had given him the same account as the one that appeared in the Orlando Sentinel, as well as additional details about what happened between the time the two came face to face and the time the gun went off.
He said he could not discuss the details on Tuesday, but said Zimmerman was sorry for what had happened.
"The George Zimmerman I know is not here anymore, because he knows that he took someone else's life, and he's extremely remorseful," Oliver said on CNN's "Starting Point."
Oliver said race played no role in the incident.
"I understand completely the fear and anger that's out there over this case. If I didn't know George Zimmerman I'd be right out there, too," he said.
"But I do know George and I do know that portrayal that young black men have had. I've experienced that growing up. I get that," said Oliver, who is African-American. "I understand that, but in this one spark incident, that wasn't the case. Race had nothing to do with it."
The Martin family and its supporters, however, have laid the blame squarely on Zimmerman, saying he racially profiled and shot an unarmed teen who was just walking back from the convenience store. They have called for changes in Florida's law and other such laws, which gun control advocates frequently refer to as "shoot first" laws.
Martin family attorney Benjamin Crump said 911 tapes, phone records and testimony from the teen's girlfriend -- who was on the phone with him just before the shooting -- show Zimmerman is to blame.
"Those facts are uncontroverted. Mr. Zimmerman and his friends can say whatever they want to say."
Crump also said authorities were trying to "demonize" Martin with news accounts that surfaced Monday, saying Martin had been suspended from school in Miami for 10 days after a search of his book bag turned up an empty plastic bag with marijuana residue.
"Whatever Trayvon Martin was suspended for had absolutely no bearing on what happened on the night of February 26," he said.
Martin's mother, Sybrina Fulton, reacted to the news this way: "The only comment that I have right now is that they've killed my son and now they're trying to kill his reputation."
Zimmerman, who has not spoken publicly about the case, is in hiding, afraid for his safety, Oliver said.
"He hasn't been back to his apartment, which is in that complex, ever since that happened, and he's being treated for post-traumatic stress disorder, for depression, for insomnia," Oliver said. "He cried for days after this happened."
CNN's Ed Payne, Kim Segal, Greg Morrison, John Couwels and Vivian Kuo contributed to this report.