By Edward Krudy

BATON ROUGE, La. (Reuters) - The U.S. Justice Department has opened a criminal investigation into the fatal police shooting of a black man in Louisiana's capital, the state's governor said on Thursday, as two deadly encounters between law enforcement and black men triggered protests in the United States.

The probe comes as community leaders in Baton Rouge urged authorities to conduct a full-scale criminal probe of two white police officers over the slaying of Alton Sterling, 37, on Tuesday.

"I want you to know that a criminal investigation is under way. It is being led by the U.S. Department of Justice," Louisiana Governor Jon Bel Edwards told hundreds of people at Living Faith Cathedral in Baton Rouge on Thursday evening.

"We are going to come out of this tragedy stronger and more united than ever," he added.

Sterling was pinned to the ground and fatally shot in the chest outside a convenience store after the officers responded to what police said was a call about a black man reported to have made threats with a gun.

The Justice Department said on Wednesday it would conduct a civil rights investigation into Sterling's death.

The city's mayor and police chief welcomed the move, but community leaders said they worried the probe would be too limited and urged authorities to consider all possible federal and state criminal charges against officers Blane Salamoni and Howie Lake.

"We don't want this to be a narrow investigation," Edgar Cage, a spokesman for the community organization Together Baton Rouge, said at a church earlier on Thursday. "We plan to use this tragic event as a tool, a stimulant to change the culture."

President Barack Obama said in a statement he had full confidence in the Justice Department's ability to conduct a "thoughtful, thorough and fair inquiry" into Sterling's death.

Citing an unnamed law enforcement official, CNN reported on Thursday that a homeless man placed the 911 call after seeking money from Sterling, who was selling CDs outside the store.

The 300-pound (135-kg) Sterling showed the man his gun and said to leave him alone, the official told CNN. Reuters could not independently confirm that account with Baton Rouge police, who did not respond to a request for comment.

Sterling, a father of five, had several criminal convictions since the mid-1990s for battery, resisting arrest, burglary and other crimes. He was a registered sex offender after spending nearly four years in prison on a charge he had sex with a 14-year-old girl when he was 20.

COMMUNITY-POLICE CHASM

Sterling's death was the first of two fatal police shootings of black men in two days. Philando Castile was shot and killed by a police officer during a traffic stop on Wednesday near Minneapolis.

The shootings and videos showing their bloody aftermath have sparked protests, including an overnight rally in Baton Rouge that drew about 300 people who stood in a peaceful vigil near the Triple S Food Mart where Sterling was killed.

Obama said that "all Americans should be deeply troubled" by the two deaths, which he said were indicative of wider problems in the U.S. criminal justice system.

At the Baton Rouge church on Thursday, Edwards said there would be a new focus on training and retraining in the police department, and stressed the need to introduce people to the police at an early age.

His words appeared to address concerns voiced by many community leaders in recent days about a chasm between the black community and the police.

Video recorded by a bystander's cellphone showed an officer confronting Sterling and ordering him to the ground. The two officers then tackled him to the pavement, with one pulling a gun from his holster and pointing it at Sterling's chest.

One officer shot Sterling five times at close range, and the other took something from his pants pocket as he was dying, another video recorded by Abdullah Muflahi, owner of the store where Sterling was killed in the parking lot, showed.

Police said Sterling was armed. Muflahi said in an interview that police took a gun out of Sterling's pocket after shooting him.

Officers Lake and Salamoni have been put on administrative leave, police said. In Lake's three years and Salamoni's four years on the force, both have been cleared by the police department after prior complaints against them regarding use of force, the Advocate newspaper reported, citing records.

The deaths of Sterling and Castile were the latest in a string of incidents in recent years involving police treatment of black men and boys in cities including Baltimore, Chicago, New York and Cleveland.

(Additional reporting by Brendan O'Brien and Bryn Stole; Writing by Colleen Jenkins; Editing by Cynthia Osterman and Peter Cooney)