Washington - Federal civil rights investigators were called in on Wednesday to probe the fatal police shooting of a black father of five in Baton Rouge, Louisiana, as the US city's mayor and police chief faced angry calls to resign.The death of 37-year-old Alton Sterling outside a convenience store in Baton Rouge was captured on cellphone video, triggering protests in the city and outrage nationwide as the United States struggles to respond to alleged police brutality against black suspects. It came on the eve of a closely watched trial in Baltimore for an officer charged in the death of Freddie Gray, a black man whose spine broke last year while he was transported in a police van.Sterling was fatally shot in the early hours of Wednesday after an anonymous caller told police they had been threatened by a man with a gun, according to a police statement.His family's lawyer said Sterling was merely selling CDs outside the Triple S store, with the permission of the shop's owner.In Baton Rouge, Louisiana Governor John Bel Edwards promised a full investigation into the "disturbing" incident, with the Department of Justice civil rights division taking the lead, assisted by the Louisiana US Attorney's office and the FBI."I have very serious concerns," Edwards told a news conference. "The video is disturbing to say the least.""I have full confidence this matter will be investigated thoroughly, impartially and professionally, and I will demand that that's the way it's conducted."'No cover-up'At an emotional press conference held earlier with relatives of the victim, the head of the civil rights group NAACP in Baton Rouge, Michael McClanahan, called for the resignations of the police chief and mayor."What we are going to do today is rule out the one percent of bad police officers that go around becoming the judge, the jury, the executioner of people period but more specifically, innocent black lives," he said. Edmond Jordan, an attorney representing Sterling's family, had demanded the investigation be carried out by an neutral third party "to ensure that there is no cover-up.""We are praying that the truth ultimately comes out from this. We think with an independent investigation we can get down to that."Video A video shot by a witness and circulated online showed two officers ordering a tall, heavy-set black man to the ground outside the convenience store. As he remained standing, the officers wrestled him onto the roof of a car and then to the ground. While he was pinned down by the officers, one pulled a gun and shot him several time at close range.The East Baton Rouge Parish Coroner's Office said Sterling was killed by multiple gunshot wounds to the chest and back, WAFB television reported.Abdullah Muflahi, owner of the Triple S convenience store who witnessed the shooting at close quarters, told The Advocate newspaper that it happened after officers hit Sterling with a Taser, which failed to bring him to the ground.An officer yelled "gun" during the scuffle with Sterling, who wasn't holding a gun or trying to reach for one, Muflahi said.Officers pulled a gun out of Sterling's pocket afterwards, he said."They were really aggressive with him from the start," Muflahi said of the police officers, adding that they were "freaking out" after the incident.Muflahi said he heard one of the officers say: "Just leave him."Police said in a statement on Facebook that Sterling was shot during an "altercation" with officers and died at the scene.In accordance with "standard procedure," the two officers involved in the shooting were placed on administrative leave during the ongoing investigation, the police said.Body camerasSuspicion over police actions grew after reports emerged that the officers' body cameras fell off during the confrontation.Authorities also seized the convenience store's video surveillance system, which apparently captured the shooting, but have yet to release any footage.About 100 people, including friends and relatives of Sterling, protested outside the convenience store after shooting, some blocking roads, The Advocate reported.Holding up handmade signs, they chanted: "Black lives matter" and "Hands up, don't shoot."'Legal lynching'Civil rights group Black Lives Matter, which was referenced by many protesters in Louisiana, tweeted: "Enough is enough. #AltonSterling."African American civil rights leader Jesse Jackson also expressed his outrage: "The shooting of #AltonSterling in #BatonRouge is a legal lynching. Justice must prevail," he wrote on Twitter.WARNING, GRAPHIC CONTENT: Video footage of the incident can be viewed here.