The NAACP leader's allegations drew sharp criticism Sunday from Robert Zimmerman Jr., who argued that FBI interviews have already shown that his brother isn't racist.
"I don't think (Jealous) does anything for civil rights by perpetuating a narrative that has now been proven false. ... They've investigated I think about three dozen of his closest friends and acquaintances. And there is not any inkling of racism. In fact, there's evidence to show the opposite," he said. "I would encourage them to cool their jets, give everyone some time to kind of process what's going on. Agitation doesn't help us. It doesn't do anybody any good right now."
The Rev. Jesse Jackson told CNN's "New Day" on Sunday that his Rainbow PUSH Coalition also wants the Justice Department to look into possible civil rights violations in the case.
"There's a Trayvon in every town," he said. "That's why the Department of Justice has a role to play, to look at this pattern, because equal protection under the law remains elusive."
The Justice Department did not respond directly to the NAACP demand. It has a separate federal investigation going on.
"Experienced federal prosecutors will determine whether the evidence reveals a prosecutable violation of any of the limited federal criminal civil rights statutes within our jurisdiction, and whether federal prosecution is appropriate in accordance with the department's policy governing successive federal prosecution following a state trial," it said in a Sunday statement.
It's a legal path that worked in the case of Rodney King, whom Los Angeles police officers clubbed down in 1991 after a car chase.
The beating of the African-American man was caught on video and later aired on news broadcasts.
When a criminal court failed to convict the white officers of police brutality, riots ensued in Los Angeles over alleged racial discrimination.
The Justice Department filed a civil rights suit against the officers, alleging racial profiling, and two were convicted in 1993 as a result.
A court sentenced them to 30 months in federal prison.