Arbery, 25, was shot to death in Brunswick, a coastal city about midway between Savannah and Jacksonville, Florida, on Feb. 23, as he was running through the Satilla Shores neighborhood.
Police have identified the two men who chased him as Brunswick resident Gregory McMichael, 64, and his son, Travis McMichael, 34. Neither has been arrested or charged, and the investigation is ongoing.
A prosecutor vowed Tuesday to bring the case to a grand jury.
But lawyers for the Arbery family said authorities don't need to wait for a grand jury to make arrests.
"There are a number of agencies that can go out and make these arrests today. That is our demand. The men who murdered Ahmaud should be prosecuted," said attorney Lee Merritt.
Merritt called on District Attorney Thomas Durden, based in Hinesville, to issue an arrest warrant and indict Gregory and Travis McMichael.
"We respect that there is a legal process that must be followed in order for formal indictments to take place, but for the safety of this community; for the respect of Ahmaud Arbery's memory we demand that ... these men be arrested," Merritt told reporters Wednesday.
The Georgia Bureau of Investigation announced Wednesday that it joined the probe at Durden's request.
"I advised him that we we would hit the ground running this morning. We've now assigned this case to three of our experienced, supervisory-level agents," GBI Director Vic Reynolds said.
"I'm confident we'll do justice in this matter."
Back on Feb. 23, Gregory McMichael first spotted Arbery on foot "hauling ass" down Satilla Drive and immediately thought he was a burglar who had recently been targeting the neighborhood, according to a Glynn County police report.
Gregory McMichael armed himself with a .357 Magnum while his son grabbed a shotgun. They both jumped into their pickup truck and chased Arbery. Police said a third man, identified as a neighbor, joined the chase and jumped into the McMichael's truck.
The older McMichael told police that he shouted at Arbery to stop. When they caught up to him, there was a confrontation.
"McMichael stated (that) the unidentified male began to violently attack Travis and the two men then started fighting over the shotgun at which point Travis fired a shot and then a second later there was a second shot,” the police report states.
The report didn't specifically say if Arbery was armed, but Merritt has said the victim did not have a weapon.
In the video of the shooting released by Merritt on Tuesday, Arbery is seen jogging down a road as a white pickup truck is stopped in front of him. Arbery runs around the vehicle and a shot is fired. The video then shows Arbery and another man appearing to tussle as two more shots are fired.
NBC News does not know what occurred before the events shown in the video.