Protests spread across the United States late Tuesday and more than 2,000 National Guard troops were deployed in the St Louis area to prevent a second night of rioting and looting after a grand jury declined to indict a white policeman in the fatal shooting of an unarmed black teenager.

President Barack Obama appealed for dialogue and his attorney general promised that a federal probe into the shooting of 18-year-old Michael Brown in August would be timely and rigorous, even as officer Darren Wilson, the policeman who shot him, said his conscience was clear.

Despite the beefed up military presence in Ferguson, a police car was torched near City Hall as darkness fell, and police fired smoke bombs and tear gas to scatter protesters. Elsewhere in the city, protests were smaller and more controlled than on Monday.

The killing in Ferguson, a predominantly black city with a white-dominated power structure, underscored the occasionally tense nature of US race relations and sometimes strained ties between African-American communities and the police.

Monday's racially charged protests were more intense than the unrest that followed the shooting itself, though were much smaller than the widespread rioting and looting that came after the acquittal of police officers in the beating of black motorist Rodney King in Los Angeles two decades ago.

In Ferguson, about a dozen buildings, including a pizza shop and a beauty parlour, were burned down late on Monday as protesters took to the streets in anger at the grand jury's decision. Police said protesters fired guns at them, set patrol cars on fire and hurled bricks into their lines. Police made 61 arrests.

On Tuesday, dozens of protesters chanted "No justice, no peace!" after dark outside the Ferguson police station, guarded by at least two armoured vehicles, and police made a handful of arrests in several locations.

About a mile away, National Guardsmen surrounded businesses damaged in Monday's violence. Groups of men also gathered on the roofs of some boarded-up stores to protect the buildings from further damage. Armed with fire extinguishers and, one said, guns, they plan to stay all night.

Protests swelled from Los Angeles to Washington on Tuesday. In New York, police used pepper spray to control the crowd after protesters tried to block the Lincoln Tunnel and Triborough Bridge and marched to Times Square. In Oakland, California, and in Atlanta, protesters blocked traffic, while in Boston others marched past a correctional facility where inmates taped Brown's name on a window in solidarity with the marchers outside.

US Attorney General Eric Holder told reporters he was disappointed by the violence in Ferguson and asked for a review to identify and isolate "criminal elements" from peaceful protesters.

Ferguson's mayor, James Knowles, lamented that the National Guard had not been deployed in enough time on Monday "to save all of our businesses."

"The decision to delay the deployment of the National Guard is deeply concerning," Knowles told a news conference. "We are asking that the governor make available and deploy all necessary resources to prevent the further destruction of property and the preservation of life in the city of Ferguson."

Missouri Governor Jay Nixon said about 700 guard troops were deployed on Monday to the Ferguson area and by late Tuesday that would be increased to 2,200 to protect homes and businesses. "This community deserves to have peace," Nixon said. "We must do better and we will."

Police were investigating as suspicious a body found in a car in Ferguson, and couldn't rule out a link between the death and the rioting. Schools in Ferguson and its surrounding cities were closed on Tuesday, as were Ferguson city offices.

"This is going to happen again," said Ferguson area resident James Hall, 56, as he walked past a smouldering building. "If they had charged him with something, this wouldn't have happened to Ferguson."

Attorneys for Brown's family condemned as biased the St Louis County grand jury process that led to the decision not to bring charges, saying the prosecutor in the case had a conflict of interest and that Wilson was not properly cross-examined.

"The process should be indicted," lawyer Benjamin Crump said, adding the Brown family wants police to be equipped with body video cameras.

The grand jury decision shifted the legal spotlight to an ongoing US Justice Department investigation into whether Wilson violated Brown's civil rights by intentionally using excessive force and whether Ferguson police systematically violate rights by using excessive force or discrimination.

Wilson, who could have faced charges ranging from involuntary manslaughter to first-degree murder, told ABC News there was nothing he could have done differently in his confrontation with Brown that would have prevented the teenager's death. "The reason I have a clean conscience is because I know I did my job right," he said, adding he would have acted no differently had Brown been white.

Wilson's lawyer, Jim Towey, later told CNN that his client's life as a police officer was over.

Documents released by prosecutors said that Wilson, who was placed on administrative leave after the shooting, told the grand jury Brown had tried to grab his gun, and that the officer felt his life was in danger when he fired.