BATON ROUGE, La. -- The mother of the son of a black man killed by white Louisiana police officers said Friday she grieved with the families of five police officers killed in Dallas during a protest over police shootings, adding she was now "walking a mile with them."

Quinyetta McMillon described herself as "very hurt" for the officers and their families.

"Now, I'm walking a mile with them. We're bearing the same shoes right now," McMillon said in an interview with The Associated Press Friday.

The Dallas protest came in response to police shootings, including the one in which 37-year-old Alton Sterling was killed Tuesday in Baton Rouge during a struggle with two police officers outside a convenience store where he was selling CDs.

Sterling was black; both officers are white. Cellphone video of his shooting was posted online and set off angry protests in Baton Rouge and beyond. The Justice Department has opened a civil rights investigation into Sterling's shooting.

Police say Sterling was armed and an eyewitness said he had a gun in his pocket. But McMillon resisted those claims Friday, saying she didn't know Sterling to carry a gun and doesn't believe he had one with him the night he was shot to death.

"I do not believe in my heart that there was a gun," she said.

McMillon said she believes police said that "to cover up something." The Baton Rouge Police Department didn't respond to the claim. The two officers involved in the shooting death, Blane Salamoni and Howie Lake II, are on administrative leave, which is customary, during the investigation.

"They should be prosecuted, the both of them. I don't want the death penalty for them. I want them to be in prison," McMillon said, calling the federal investigation a "very positive step."

McMillon called Sterling a good father to their son Cameron, 15, who broke down in sobs at a rally outside City Hall earlier this week. She said Cameron Sterling has been devastated by the loss.

"I called them the Doublemint twins because they both liked snacks. They both like to eat, so they was always eating something" when they spent time together, which was regularly, McMillon said.

Her face lighting up with a slight smile as she talked, McMillon said Alton Sterling was close to their son. She recalled when Cameron Sterling took his first steps, Alton Sterling swooped in to catch his son each time he wobbled, to keep him from hurting himself when he fell. She said it's one of her best memories.

"Every second my son goes to stumble, he's breaking his neck to get to him," McMillon said. "And that memory will never be forgotten, because right now I use that same memory in terms of coping with my son and letting him know right now, 'You still pick yourself up."'

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.

McMillon focused on Sterling's smile, saying people knew he was a "good, genuine man." Prior cases aren't relevant, she said.

"As far as his criminal record, it has nothing to do with right now. That is the past," she said. "Right now, we're focusing on what happened to him."

Protesters have gathered for three nights at the Triple S Food Mart where Sterling was shot to death as they tried to make sense of recent events, including a fatal shooting in Minnesota, in which Philando Castile's girlfriend streamed video to Facebook after he was shot by a police officer Wednesday. Castile also was black.

Cornell William Brooks, the national head of the NAACP, visited Baton Rouge on Friday and said he is tired of victims of police shootings being treated as "hashtag tragedies" instead of human beings mourned by their families.

Asked about how the shootings reflect on race relations across the nation, McMillon said she didn't want Sterling's shooting to "be a race thing." She wouldn't answer questions, however, about whether she believed police would have responded the same way if Alton Sterling had been white.

After the shootings of police officers in Dallas, McMillon said she hoped the Baton Rouge protests would remain peaceful. More protests were planned throughout the weekend.

Baton Rouge Police Chief Carl Dabadie Jr. said his department has strived to avoid a "military-style response" to the protests.

State and local law enforcement officials briefed Louisiana Gov. John Bel Edwards on Friday about their public safety strategies. Louisiana State Police Col. Mike Edmonson said officials reviewed with the governor what assets were available to law enforcement and how quickly they can be mobilized in an emergency.

Associated Press writers Rebecca Santana, Cain Burdeau and Kevin McGill in New Orleans contributed to this report.