(CNN) -- The separatist New Black Panther Party, described as a hate group by a civil rights organization, is standing by its $10,000 bounty offer for the capture of the man who shot Trayvon Martin, despite vehement opposition from, among others, Martin's family.
"We're here to make them do their job," organizer Mikhail Muhammad said on Monday. "We will support Trayvon's family, but we are military."
Martin was shot February 26 by George Zimmerman, a 28-year-old neighborhood watch volunteer, while walking back from a Sanford, Florida, convenience store. Zimmerman, according to friends and his attorney, Craig Sonner, said he killed Martin, 17, in self-defense.
The fact he hasn't been charged in Martin's killing has outraged many in the United States, including people who believe Martin was considered "suspicious" because he was black. Zimmerman is a white Hispanic.
Yet no one has gone as far as the New Black Panther Party, which on its website advocates a revolution for African-Americans. The group -- which is distinct from the better known Black Panther Party, founded in the late 1960s -- is described by the Southern Poverty Law Center as a hate group and a "virulently racist and anti-Semitic organization."
On Saturday, the party put out a wanted poster offering money in return for a "legal citizen's arrest" of Zimmerman. Muhammad said that same day that his group believed in "a life for a life," an assertion that he reiterated on Monday.
Martin family attorney Daryl Parks echoed comments by others associated with the family, including the Rev. Jesse Jackson, condemning the apparent bounty offer. "We don't condone those people whatsoever," Parks said.
Speaking earlier Monday to city officials in a packed Sanford Civic Center, Trayvon's father, Tracy Martin, said his family wanted to work through the legal system and spur changes in Sanford's police department and Florida law.
"We're not asking for an eye for an eye," Tracy Martin said. "We're asking for justice, justice, justice."
Mohammad said the U.S. Constitution grants people the right to make a citizen's arrest, although he also said, a short time later, that he doesn't "obey the white man's law, I don't follow the American law."
"According to the street people's law, (George Zimmerman) has been charged with murder -- according to street law, according to God's law," Muhammad said.
The city of Sanford earlier responded to the bounty offer, and the New Black Panther Party's push to have 5,000 men work together to go after Zimmerman, by calling for "calm heads and no vigilante justice."
"Attempts by civilians to take any person into custody may result in criminal charges or unnecessary violence," the department said.
Joe Oliver, a friend of Zimmerman's, said such threats are weighing heavily on his friend, even if authorities and the Martin family are denouncing them. Zimmerman hasn't been seen or heard from in public since the shooting,
"That's why no one knows where he's at," Oliver said. "He should be concerned for his safety."
Oliver, a CNN anchor in the 1990s, said he's worried himself because he has spoken on several media outlets about the case.
"I now have to be concerned for my safety, not just for myself but for my friends and family as well," he said. "Yet I wasn't there, I didn't pull the trigger. All I'm doing is standing up for a friend."