The officer's shooting comes after Ferguson Police Chief Tom Jackson issued a videotaped apology earlier in the week and attempted to march with protesters, an effort that led to a clash with activists and several arrests on Thursday.
Messages left with Jackson and spokesmen Saturday night were not immediately returned.
A county grand jury is weighing whether to indict Ferguson officer Darren Wilson in Brown's shooting.
The Justice Department, which is investigating whether Brown's civil rights were violated, is conducting a broader probe into Ferguson police. On Friday, it urged Jackson to ban his officers from wearing bracelets supporting Wilson while on duty and from covering up their name plates with black tape.
Ferguson residents complained about the bracelets, which are black with "I am Darren Wilson" in white lettering, at a meeting with federal officials this week.
But the parents of Michael Brown said that they were unmoved by the apology given by the Ferguson police chief.
Brown's mother, Lesley McSpadden, said, "Yes," when asked if Chief Tom Jackson should be fired, and his father, Michael Brown Sr., said rather than an apology, they would rather see Officer Darren Wilson arrested for the death of their son on Aug. 9.
"An apology would be when Darren Wilson has handcuffs, processed and charged with murder," Brown Sr. said.
The young man, who was black, was fatally shot last month by Wilson, who is white.
The shooting sparked days of violent protests and racial unrest in the predominantly black community. Some residents and civil rights activists have said responding police officers were overly aggressive, noting their use of tear gas and surplus military vehicles and gear. The shooting and police response to the protests stoked a national discourse about police tactics and race
Brown Sr. called the looting that has been interspersed with the protests "disrespectful," but the "First Amendment protesting? They have that right." The First Amendment of the US Constitution guarantees such basic rights as freedom of speech and assembly.
"There's going to continue to be unrest until they do what should be done," McSpadden added, referring to Ferguson officials.
Jackson released a video apology to Brown's family and the community, which is predominantly African-American, in which he acknowledged that Brown's body should have been removed from the street much sooner than it was. The young man's remains lay uncovered for more than four hours while police collected evidence.
"I don't want words, I want action," McSpadden said.
The parents, both wearing t-shirts with messages about their son, talked hesitantly about their emotions following their son's death. McSpadden said she feels lost and helpless, and her life will never be normal again. "I have to find a new normal," she said haltingly.
"I'm empty," Brown said quietly. "There's nothing there anymore. It's hard to fill that spot with other happiness."
Brown's parents are in Washington, D.C., to meet with lawmakers and lobby Congress to pass a law requiring police officers to wear cameras during their interactions with the public. They also called on the Justice Department to take over the criminal investigation into the shooting. The Justice Department is already investigating whether Brown's civil rights were violated, and a county grand jury is weighing whether to indict Wilson.
"All of our eyes see the same thing, that it was wrong, an injustice. Why wouldn't they come back with an indictment?" McSpadden said.
Attorney General Eric Holder has met with Brown's parents, and they hope his upcoming departure will not affect the case. Holder announced his resignation Thursday. "I've got confidence in him in that he will make sure that what needs to be done is done before he exits," McSpadden said.
The parents also expressed anger at some Ferguson police officers who wore bracelets in support of Wilson. In a letter released Friday, the Justice Department asked Jackson, the police chief, to "confirm our understanding" that officers in the suburban St. Louis County department won't wear "I am Darren Wilson" bracelets while on duty.
Ferguson residents complained about the black bracelets with white lettering this week at a meeting with federal officials. The Brown family's lawyer, Benjamin Crump, said the bracelets give an impression that the police lack impartiality in this case.
"It lets me know how they really feel about the situation, and the wrongness that they do," McSpadden said.
Brown's parents talked with lawmakers during the Congressional Black Caucus' legislative conference weekend and plan to keep on lobbying. "I ask Crump all the time, 'What else can I do?' McSpadden said.
Brown Sr. called their efforts a fight for human rights. "They say that this is America, but we're not being treated like we're Americans. Our fight here is to just open other eyes and understand how we're feeling and try to get something done about it," he said.
McSpadden said her son was taught how to respect his elders.
"I taught my son respect for a policeman, for you, for this woman, for anybody, so if he felt like he was doing nothing wrong, which I don't believe he was, why would he be in fear of him? You're not supposed to fear the police."
-AP
