The McMillian Campaign / Reuters

Marco McMillian, a candidate for mayor of the Mississippi Delta city of Clarksdale, is shown in this undated campaign photograph released to Reuters on Feb. 27, 2013.

The FBI said Thursday that it was monitoring the investigation into the killing of a black and openly gay mayoral candidate in Mississippi whose burned and beaten body was found on the Mississippi River levee outside town last week.

Marco McMillian, a candidate for mayor of Clarksdale, population about 20,000, was found dead last Wednesday. His family said he was beaten, dragged and set ablaze -- a death that "was not a random act of violence," they said in a statement. 

Authorities have arrested Lawrence Reed, who is also black, and charged him with murder in connection with the case. They say the killing is not being handled as a hate crime, though the FBI could determine whether to file a federal hate crime charge, which covers acts motivated by bias against sexual orientation, The Associated Press reported.

Mississippi’s hate crimes law does not cover acts motivated by sexual orientation.

After learning of the circumstances surrounding McMillian's death, special agents from the FBI's Jackson division made contact with the local sheriff's department and the Mississippi Bureau of Investigation last Friday.

"In this case, the FBI will continue its ongoing dialogue and sharing of information with the local and state agencies, and will continue to monitor this investigation for any indication that a potential violation of federal law exists," Daniel McMullen, special agent in charge of the FBI for Mississippi, said in a statement.

Related: Mayoral candidate's death shocks Mississippi town 

The candidate's sport-utility vehicle was involved in a head-on collision in Coahoma County in the Mississippi Delta early last week. Reed had been driving when the accident occurred, but McMillian was not in the vehicle, triggering a search for him, according to media reports.

McMillian had moved back home from Memphis in January to vie for office as a Democrat. He was one of the first viable openly gay candidates to run for office in Mississippi, according to the Victory Fund, a national organization that supports gay and lesbian candidates.

Friends said his sexual orientation was known and was not an issue, according to a local newspaper, The Clarion Ledger.

On Sunday, McMillian's family said in a statement his body was “beaten, dragged and burned,” indicating that he had been pulled behind a car. 

The Associated Press and Reuters contributed to this report.