By Carey Gillam

FERGUSON Mo. (Reuters) - President Barack Obama called the police shooting death of an unarmed black teenager a tragedy and called on Tuesday for thoughtful response after two nights of violent protests, looting, arrests and tear gas in a St. Louis suburb.

He promised a full investigation by the U.S. Department of Justice into the case, which has provoked outrage in the largely African-American town of Ferguson where police have not released the shooter's name, citing security concerns and death threats.

"I know the events of the past few days have prompted strong passions, but ... I urge everyone in Ferguson, Missouri, and across the country, to remember this young man through reflection and understanding," Obama said in a statement.

Friends and family of 18-year-old Michael Brown planned a peaceful church vigil for Tuesday night and his father pleaded for an end to the violence that has followed the incident, while activists demanded authorities release the name of the officer involved.

Standing with supporters, including the Rev. Al Sharpton, Michael Brown Sr. said he wanted justice for his son but wanted it "the right way."

"I need all of us to come together and do this right, the right way," said Brown Sr., who wore a T-shirt showing his son's baby picture. "No violence."

Activists speaking to reporters in downtown St. Louis also called for federal authorities to take over the investigation after two nights of demonstrations and unrest.

Police in Ferguson, Missouri, had initially said they would release the officer's name on Tuesday, but changed the plan, citing fears of retaliation, according to media reports.

Sharpton, a New York-based civil rights leader, also called for peaceful protest in the wake of looting and more than 50 arrests since the shooting. Sharpton's National Action Network will pay for Brown's funeral.

"To become violent in Michael Brown's name is to betray the gentle giant that he was," Sharpton said of the 6-foot, 4-inch (198-cm) Brown, who had planned to start college this week. A demonstration is planned at a Ferguson-area church on Tuesday evening.

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Brown was shot to death in the back of a police car on Saturday, police said. The race of the officer, a six-year veteran who is now on administrative leave, has not been revealed.

The FBI has opened a civil rights investigation into the racially charged case and St. Louis County also is investigating.

Police said Brown was shot in a struggle with a gun in the police car but have not said why Brown was in the car. At least one shot was fired during the struggle and then the officer fired more shots before leaving the car, police said.

CONFLICTING ACCOUNTS

But a witness to the shooting interviewed on local media has said that Brown had been putting his hands up to surrender when he was killed.

"There were many, many witnesses who have talked to family members and they paint a very different picture than police witnesses," said Benjamin Crump, an attorney for the Brown family. Crump also represented the family of Trayvon Martin, an unarmed black teen killed in Florida by a neighborhood watch volunteer in 2012.

The "hands up" gesture has been frequently seen at protests over the shooting. More than 100 protesters in front of the St. Louis County Courthouse in nearby Clayton on Tuesday morning chanted "hands up, don't shoot."

The Federal Aviation Administration issued a ban on air traffic under 3,000 feet above Ferguson starting Tuesday. The order said the ban was "to provide a safe environment for law enforcement activities." Such bans are typically requested by police departments so that their aircraft do not tangle with news helicopters.

Residents in the low-income, mostly black neighborhood where Brown was killed say they are often harassed by police. Ferguson Police Chief Tom Jackson said the neighborhood had a lot of crime but there were no race problems.

Demonstrations on Sunday night turned violent, with looting and property damage. Violence broke out again on Monday night as police officers in riot gear, armed with rifles and accompanied by dogs tried to secure the area.

Ferguson has seen a stark demographic shift in recent decades, going from all white to mostly black. About two-thirds of the town's 21,000-strong population are black, while out of a police force of 53, three officers are black.

The race of officers should not matter as long as their work is fair and professional, said Dave Klinger, a former police officer and criminal justice professor at the University of Missouri-St. Louis.

"If the officer behaved inappropriately, we've got to sanction the officer and figure out what it is that led him to do what he did," Klinger said. "Was he poorly trained? Was there a pattern in this agency?"

Klinger said the investigation must be as "transparent as possible."

(Additional reporting by Mary Wisniewski in Chicago; Writing by Eric M. Johnson and Mary Wisniewski; Editing by Susan Heavey, Bill Trott and Eric Walsh)