The U.S. Justice Department is considering federal charges of hate crimes for the death of unarmed athlete Ahmaud Arbery, Georgia, in February.
Gregory McMichael and his son Travis, who are white, are facing charges of murder and assault because of the shots.
The case sparked national outrage when the death video appeared last week.
Arbery's supporters are using the hashtag #IRunWithMaud, sharing photos and running 3.63 km on the day he died, on February 23.
Some held protests outside the courts in Georgia and neighboring Florida.
Questions were raised as to why the police failed to charge the McMichaels for more than two months. The two were detained on Thursday by the State Department of Investigation (GBI), two days after the video was released.
Gregory, 64, and Travis, 34, are in the custody of the Glynn County Sheriff's Department, officials said on Friday.
What did the justice department say?
The department said it would take "any appropriate action justified by the facts and the law", in a statement tweeted by spokeswoman Kerri Kupec.
"The Department of Justice's Civil Rights Division, the FBI and the South Georgia District Attorney are supporting and will continue to support and participate fully in the state investigation," the statement added.
"We are evaluating all the evidence to determine whether federal hate crime charges are appropriate."
What is the status of the investigation?
Georgia bailiffs promised to investigate why it took so long to arrest the McMichaels.
GBI director Vic Reynolds told reporters on Friday that "all stones will be delivered, I promise".
He said the individual who shot the video – another local man – was also under investigation.
Last Tuesday, Atlantic Circuit District Attorney Tom Durden decided that a grand jury should consider the case and accepted Governor Brian Kemp's offer for the GBI to investigate. Two days later, GBI said it had arrested the McMichaels.
Durden is the third prosecutor involved, when two district prosecutors withdrew due to professional connections with Gregory McMichael.
Mr. McMichael, the elder, was a police officer in Glynn County for seven years, before working as an investigator in the district attorney's office for 24 years. He retired a year ago.
The shooting led to a wave of outrage from national figures, including presidential candidate Joe Biden and basketball star LeBron James.
Biden said Arbery was "slaughtered in cold blood" and "essentially lynched before our eyes".
James tweeted: "We are literally hunted EVERY DAY / EVERY DAY, we leave the comfort of our homes!"
How Arbery died?
Arbery went for a run in the city of Brunswick in the early afternoon of February 23 – something his father said he used to do.
Gregory McMichael told police he believed Arbery looked like the suspect in a series of local raids.
McMichael and his son armed themselves with a pistol and shotgun and chased Arbery in a pickup truck in the Satilla Shores neighborhood.
McMichael, the eldest, told police he asked Arbery to stop and talk and said the 25-year-old attacked his son.
The 36-second clip appears to show young McMichael firing a shotgun at close range at Arbery and the victim falling on the street.