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Armed National Guards have been deployed on the streets of the Californian city, where many of the shops and businesses now lie in smouldering ruins.
About 500 businesses, most of them white-owned, are reported to have been destroyed or damaged in what is a predominantly black neighbourhood.
The trouble began in the Watts area of the city four nights ago when a black man was stopped on suspicion of drunken driving.
A crowd gathered around the car as the driver and his brother began arguing with the police officers. Their mother then joined the argument. When all three were arrested the trouble began.
The crowd began throwing bricks and bottles. Shop windows were broken and stock looted. Black youths ran through the streets setting fire to churches, offices and other buildings.
The Governor of California, Edmund Brown, who has just flown back from Europe, said: "We are involved in a state of insurrection there."
William Parker, the police chief of Los Angeles, said: "We haven't the slightest idea when this can be brought under control."
Over the weekend, sniping and looting have continued. The cost of repairs is now put at $100m.
Television pictures show black shopkeepers have posted notices on their businesses reading "Blood brother" or "Negro-owned" in an attempt to prevent attacks on the premises.
One National Guard officer was injured when he was hit by a car reportedly driven by a black man. After that incident, officers were authorised to load their rifles and attach bayonets.
Some 18,000 National Guards have been deployed. About 2,000 were flown in from San Francisco.
President Lyndon Johnson, who spent the weekend at his Texas ranch, has called for an end to the violence.
He said: "Killing, rioting and looting are contrary to the best traditions of this country.
"Every person has the responsibility to uphold law and order. I call upon all Americans to fulfil that responsibility."
Civil rights leader Martin Luther King is on his way to Los Angeles. He claims the poor social conditions are the underlying cause for the discontent.
In 1964 the United States passed the Civil Rights Act, which was intended to herald a new era in race relations. But many states acted quickly to circumvent the law. California blocked the fair housing legislation thus ensuring segregation continued.
It led to a great feeling of injustice and resentment in the inner cities. The riots in Los Angeles lasted six days, left 34 dead and about 1,000 people injured. Nearly 4,000 people were arrested and hundreds of buildings were destroyed.
A commission headed by former CIA Director, John McCone, concluded the riots were the result of many socio-economic problems like unemployment, poor housing and lack of education, but little was done to address the problems.
The California Advisory Committee to the US Commission on Civil Rights claimed the report's findings were superficial and showed a lack of understanding of the civil rights movement. It also criticised the report's failure to address the issue of police malpractice.
Los Angeles was the scene of another riot in 1992, triggered by the acquittal of four white police officers accused of beating a black motorist, Rodney King.
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