Ibragim Todashev, 27, overturned a table and lunged at the agent but had no weapon, two law enforcement officials told The Washington Post.
Some law enforcement officials initially said Todashev brandished a knife and others suggested he tried to grab the FBI agent's gun.
The FBI refused to comment on the latest report, saying in a statement it "takes very seriously any shooting incidents involving our agents and as such we have an effective, time-tested process for addressing them internally."
"The review process is thorough and objective and conducted as expeditiously as possible under the circumstances," the statement said, explaining the review could take several months.
The Florida chapter of the Council on American-Islamic Relations, before the Post report, cited FBI sources as saying Todashev was unarmed when he was killed May 22. The civil rights advocacy organization called for an independent investigation by the Justice Department's Civil Rights Division.
The division is responsible for enforcing federal statutes prohibiting discrimination on the basis of race, sex, disability, religion or national origin.
The division and local prosecutors are already reviewing the case, officials told the Post.
CAIR-Tampa Executive Director Hassan Shibly said in a news conference in Orlando, Fla., Wednesday evening Todashev was hit by bullets seven times, including once in the head.
He showed what he said were photos of Todashev's body after the shooting. The photos were taken at an Orlando funeral home after the local medical examiner's office released the body to Todashev's next of kin, he said.
"We want to know why it happened. ... We want to know what is the truth," Reniya Manukyan, Todashev's widow, said at the news conference in remarks quoted by the Orlando Sentinel.
The FBI said in a statement the day of the shooting Todashev, a former Boston resident who the FBI did not initially identify, was killed during an interview with the FBI agent, two Massachusetts State Police troopers and other law enforcement personnel.
The investigators were questioning him about how he knew bombing suspect Tamerlan Tsarnaev and about the possible role he and Tsarnaev had in a Sept. 11, 2011, triple murder near Boston, the May 22 statement said.
Officials said they suspected Todashev and Tsarnaev, the older of the two suspected Boston Marathon bombers, may have had a role in cutting the throats of three men in Waltham, Mass.
Officials said Todashev was not suspected of involvement in the April 15 Boston bombing.
Tsarnaev was killed in a shootout with police four days after the bombing. His younger brother, Dzhokhar Tsarnaev, was captured later that day and remains in custody.
Manukyan said Wednesday she had records proving her husband was with her in Atlanta Sept. 11, 2011, so he could not have been in Massachusetts.
The May 22 FBI statement said a "violent confrontation was initiated by the individual" during the daylong interview, prompting the fatal shooting.
The agent sustained non-life-threatening injuries in the confrontation, the FBI said then. Those injuries were later described by a law enforcement official as "some cuts and abrasions," the Post said.
An official cited by the Post said the other law enforcement officials had stepped out of the room shortly before the confrontation occurred, leaving the FBI agent alone with Todashev.