FALCON HEIGHTS, Minn. -- The fatal shooting of a black man in his car by a Minnesota police officer went viral Thursday, its aftermath broadcast live over Facebook by the victim's girlfriend, who cried that he had just been shot "for no apparent reason."

The shooting happened late Wednesday during a traffic stop in the St. Paul suburb of Falcon Heights.

In the video, the woman describes being pulled over for a "busted tail light" and says her boyfriend had told the officer he was carrying a gun for which he was licensed. She says he was shot as he reached for his wallet.

As word of the shooting spread, relatives of the man joined scores of people who gathered at the scene and outside the hospital where he died. They identified him as Philando Castile of St. Paul, a cafeteria supervisor at a Montessori school.

Castile's girlfriend said Thursday that he was killed even though he complied with the officer's instructions. Diamond Reynolds told reporters that Castile did "nothing but what the police officer asked of us, which was to put your hands in the air and get your license and registration."

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Minnesota Gov. Mark Dayton told reporters that he asked the White House to begin a Justice Department probe into Castile's death. The state Bureau of Criminal Apprehension opened its own independent investigation overnight, he said.

A law enforcement source told CBS News that the Justice Department will monitor the state investigation but not take it over at this time, CBS News senior investigative producer Pat Milton reports. The official said the Justice Department will independently assess what further action may be warranted.

Investigators from the Minnesota Bureau of Criminal Apprehension inspect a car in which a passenger was fatally shot by a police officer during a traffic stop in the St. Paul suburb of Falcon Heights on July 6, 2016. CBS Minnesota

The Facebook Live video was posted Wednesday night to Reynolds' page under the name "Lavish Reynolds." It shows Reynolds in a car next to a bloodied Castile slumped in a seat. A clearly distraught armed police officer stands at the car's window, telling Reynolds to keep her hands where they are and intermittently swearing.

In the video, the officer tells Reynolds to keep her hands up and says: "I told him not to reach for it. I told him to get his hand out."

"You shot four bullets into him, sir. He was just getting his license and registration, sir," Reynolds responds.

The video goes on to show Reynolds exiting the car and being handcuffed. A young girl can be seen and is heard saying at one point, "I'm scared, Mommy."

Reynolds describes being put in the back seat of the police car and says, "The police just shot my boyfriend for no apparent reason."

A handgun was recovered from the scene, police said.

The interim police chief in nearby St. Anthony, Jon Mangseth, said this morning that he was "made aware there was a livestream on Facebook" but that he did not know anything about its contents. He has not commented on it further.

Castile's mother, Valerie Castile, lost her only son in the shooting, Ashley Roberts of CBS Minneapolis station WCCO-TV reported on "CBS This Morning."

"He did everything by the law, and he died by the law," Valerie Castile told CBS.

Philando Castile's mom Valerie: "He lived by the law & died by the law." #FalconHeights pic.twitter.com/sgs7bdYFlG — Jennifer Mayerle (@jennifermayerle) July 7, 2016

"It's just like we're animals," Castile's sister Alize Castile told CBS. "It's basically modern day lynching that we're seeing going on except we're not getting hung by a tree anymore - we're getting killed on camera."

Speaking to CNN early Thursday, Castile's mother said she suspected she would never learn the whole truth about her son's death.

"I think he was just black in the wrong place," Valerie Castile said, adding that she had underlined to her children that they must do what authorities tell them to do to survive.

"I know my son ... we know black people have been killed ... I always told them, whatever you do when you get stopped by police, comply, comply, comply."

Castile's exact age was not immediately clear. Relatives said he was 32. Reynolds said he was to turn 35 later this month.

Police did not release any details about the officer who fired except to say he had been placed on paid administrative leave. Reynolds described him as Asian.

Castile's uncle, Clarence Castile, told reporters he had a message for the officer.

"You, wherever you're at, your time is coming," Castile said. "You need to fess up. Tell the truth. Tell the truth, and the truth will set you free."

It was the second fatal shooting this week, coming only days after a black 37-year-old man was killed by officers in Baton Rouge, Louisiana. Alton Sterling's death was caught on video.

On Wednesday, the Justice Department launched a civil rights investigation into Sterling's shooting, which took place after he scuffled with two white police officers outside a convenience store.

White House press secretary Josh Earnest told reporters traveling on Air Force One that President Obama was "deeply disturbed" by reports of this week's police shootings. Mr. Obama, who was traveling to Poland to meet with NATO leaders, was following the situation in Baton Rouge and Minnesota, Earnest said.

Castile's cousin, Antonio Johnson, told the Star Tribune that because Castile was a black man driving in a largely middle-class suburb, he "was immediately criminally profiled and he lost his life over it."

The site of the shooting in Falcon Heights is close to the Minnesota State Fairgrounds and not far from a clutch of fields associated with the University of Minnesota's agricultural campus.

Late Wednesday, protesters moved to the governor's mansion in nearby St. Paul, where around 200 people chanted and demanded action from Dayton, a Democrat. By daybreak, around 50 protesters remained outside the mansion despite a light rain.

Reynolds addressed reporters outside the mansion, and her comments were streamed on Facebook.

Clarence Castile spoke to the Star Tribune from the Hennepin County Medical Center, where he said his nephew died minutes after arriving.

He said Philando Castile had worked in the J.J. Hill school cafeteria for 12 to 15 years, "cooking for the little kids." He said his nephew was "a good kid" who grew up in St. Paul.

Castile started working for St. Paul's school district in 2002 and was promoted to his supervisory position two years ago, according to the district.

Minnesota court records online show Castile had some misdemeanor violations, mainly related to driving.

The president of the Minneapolis NAACP, Nekima Levy-Pounds, told the crowd she has no faith in the system in the wake of this and other police shootings of black men.

"I'm tired of the laws and policies on the books being used to justify murder," Levy-Pounds, a civil rights attorney, said as rain began to fall. "This is completely unacceptable. Somebody say, 'Enough is Enough.'"