BATON ROUGE, La. -- An investigation into the police shooting death of a black man in Baton Rouge found that there was not enough evidence to prove that the white officers acted unreasonably and willfully, a federal prosecutor said Wednesday, as the man's family spoke out.

The Justice Department's decision may not be the final legal chapter, however, because state authorities can conduct their own investigation of Alton Sterling's death last summer and possibly pursue state charges.

U.S. Attorney Corey Amundson described the federal investigation at a news conference after meeting with Sterling's family, saying every agent and prosecutor involved in the probe believed charges were not warranted for Officers Blane Salamoni and Howie Lake II.

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Sterling, 37, was selling homemade CDs outside the Triple S Food Mart when police were called to the store to investigate a report of a man with a gun. Two cellphone videos of Sterling's struggle with the two officers quickly spread on social media after the shooting.

Amundson said the officers' encounter with the 6-foot-3, more than 300-pound Sterling happened in the span of about 90 seconds.

"Life and death decisions were being made in split seconds," he said.

The investigation found that Salamoni shot Sterling three times after saying that Sterling was reaching for a gun in his pocket and he fired three more shots into Sterling's back when he began to sit up and move, the prosecutor said.

The officers recovered a loaded revolver from Sterling's pocket. Two independent use-of-force experts reviewed the case and criticized the way the officers handled the situation but did not find that they acted excessively, Amundson said.

Alton Sterling in Facebook photo. WAFB-TV/Facebook

CBS News' Paula Reid reported Tuesday that the Justice Department was expected to close the investigation into Sterling's death and bring no charges in the case. On Wednesday, the family of Sterling spoke to reporters at about the same time as the DOJ's announcement.

"I want to tell y'all some of the hurt I had yesterday," said Sanda Sterling, Alton's aunt, who raised him, CBS Baton Rouge affiliate WAFB reports. "I was at work and when I got back to my car and I seen my phone blowing up I couldn't believe what I heard on the phone. I'm on the interstate and I lost it, I panicked. So yesterday, to me was the first day that it happened. I went back to July 5 at 1:30 in the morning. I suffered all day yesterday. I suffered. What I heard today... the suffering still continues. So now that I know there is not a civil matter anymore, now it's a human matter."

Sterling's son Cameron said, "I just want to let everybody know no matter what goes on behind closed doors in that court, it doesn't matter. We still have to depend on God."

"I have my brothers and sisters to look after. Eleven of them," Cameron said, according to WAFB. "I have to look after every last one of them because guess what, I'm that next legacy. I'm here after my dad. My dad is now long gone, so now I'm here so I'm that legacy and I have to look after those kids."

Family and community members also spoke out on Tuesday night. During a vigil at the site where Sterling was killed, many expressed disappointment, CBS New Orleans affiliate WWL reported.

Residents and community activists held hands and prayed before urging state authorities to step in and take action. Some called for Louisiana Attorney General Jeff Landry's office to investigate. Mya Richardson, an 18-year-old activist, read out Landry's Twitter handle and office phone number over a microphone and urged the crowd to "show him how angry you are."

Raheejah Flowers, 16, fought back tears as she told the crowd that "this is not the end."

"We are not going to take this sitting down," she said. "Alton did not die here for us to suck it up and move on!"

Sterling's killing last year was captured on cellphone video and circulated widely online, sparking demonstrations across Baton Rouge. Police arrested nearly 200 protesters in the city following Sterling's death, which occurred a day before another black man was killed by police in Minnesota.

Louisiana Gov. John Bel Edwards immediately asked for a federal investigation of Sterling's death. He called cellphone video of the incident "disturbing, to say the least."

Chris Stewart, a lawyer for two of Alton Sterling's sons, told reporters Wednesday that the white officer who shot Sterling pointed a gun at the black man's head and threatened to shoot him before they struggled. Stewart said that he was told in a meeting with Department of Justice officials that Salamoni walked up to Sterling, pointed a gun to his head and said "I'm going to shoot you, b****."

Stewart provided that account shortly after Amundson's news conference.

Amundson did not mention the alleged threat and did not take questions. John McLindon, Salamoni's lawyer, said he could not comment on the allegations.

The decision in the Sterling case was the highest profile decision not to bring charges against police officers in a deadly shooting since Jeff Sessions became attorney general. But the federal investigation into possible civil rights violations by the officers was seen as problematic. Authorities in such cases must meet a difficult standard of proof, a challenge that has complicated prosecutions in past police shootings.

As a convicted felon, Sterling couldn't legally carry a gun. Court records show Sterling had pleaded guilty in 2011 to being a felon in possession of a firearm and illegally carrying a weapon and was arrested in May 2009 after an officer confronted him outside another store where he was selling CDs.

Both officers remain on administrative leave, a standard procedure.