Some 2,000 National Guard troops helped ward off a second night of rampant arson and looting in suburban St Louis after a grand jury declined to indict a white policeman in the fatal shooting of an unarmed black teenager, and sympathy protests spread to several US cities.

President Barack Obama appealed for dialogue, and his attorney general promised that a federal probe into the August 9 killing of 18-year-old Michael Brown in Ferguson, Missouri, would be rigorous.

Officer Darren Wilson, the policeman who shot him, said his conscience was clear.

Despite a 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.

A crowd of demonstrators later converged near police headquarters, scuffled with officers who doused them with pepper spray, then smashed storefront windows as they fled under orders to disperse. But the crowds were smaller and more controlled than on Monday, when about a dozen businesses were torched and others were looted amid rock-throwing and sporadic gunfire from protesters and volleys of tear gas fired by police. More than 60 people were arrested then, compared with 44 arrests on Tuesday night, police said.

"Generally, it was a much better night," St. Louis County Police Chief Jon Belmar told reporters early Wednesday, adding there was very little arson or gunfire, and that lawlessness was confined to a relatively small group.

Police and Guard troops mounted a vigorous defense of City Hall out of concern it might come under attack by arsonists, but damage to the building was limited to some shattered windows, Belmar said.

"We saw some protesters out there that were really out there for the right reason," he said. "Unfortunately, there seems to be a few people who are bent on preventing this from happening in the most ideal way that it could."

The unrest surrounding Brown's death in Ferguson, a predominantly black city with a white-dominated power structure, underscored the often-tense nature of US race relations and strained ties between African-American communities and police.

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

An enlarged contingent of National Guard troops 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 planned to stay all night.

Elsewhere, protests swelled from Los Angeles to Washington DC 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. Several hundred also marched in Harlem, chanting "Racist police!"

Protesters in Los Angeles threw water bottles and other objects at officers outside city police headquarters and later obstructed both sides of a downtown freeway with makeshift roadblocks and debris, authorities said.

In Oakland, California, protesters set rubbish on fire in the middle of a street and swept onto a downtown stretch of Interstate 980, briefly halting traffic. Demonstrators also blocked traffic in Atlanta, where 21 arrests were reported.

Four people were arrested for blocking a roadway in Denver, where police said several hundred people turned out for a protest march. In one of the night's biggest rallies, an estimated 1,500 people took to the streets of Boston, though police there reported just a handful of arrests. Inmates at a correctional facility in Boston taped Brown's name on a window in solidarity with protesters.