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Violence erupted in cities across the US on the sixth night of protests sparked by the death in police custody of African-American George Floyd.
Trump said he told state governors it was time to dominate the streets with overwhelming security presence.
If cities refused he would deploy the US military and quickly solve the problem for them, he said.
He said attacks on police by protesters were acts of domestic terror.
Largely peaceful protesters near the White House were repelled with tear gas and mounted police on as Trump spoke in the Rose Garden, live televised images showed.
Trump said he was mobilising all federal resources to suppress the protests.
Dozens of cities imposed curfews, but many people ignored them, leading to stand-offs and clashes.
Riot police faced off with protesters in New York, Chicago, Philadelphia and LA, firing tear gas and pepper bullets to try to disperse crowds.
Police vehicles were set on fire and shops were looted in several cities.
The country is experiencing the most widespread racial turbulence and civil unrest since the backlash to the assassination of Martin Luther King in 1968.
The outpouring of anger began last Tuesday, after a video showed George Floyd being arrested in Minneapolis and a white police officer continuing to kneel on his neck even after he pleaded he could not breathe and fell unconscious.
The National Guard - the US reserve military force for domestic emergencies - said on Sunday that 5000 of its personnel had been activated in 15 states and Washington, DC, where crowds once again gathered near the White House.
Demonstrators lit fire to buildings there, including a historic church known as the church of the presidents, and threw stones at riot officers. Police used tear gas in response.
In Louisville, Kentucky, a man was shot dead in a confrontation between protesters, police and the National Guard after midnight early on Monday. Shots were fired at police officers and guard troops as they moved to disperse a crowd in a car park and "returned fire", leaving one man dead, Louisville Metro Police said.
Trump tells governors to get tougher on protesters
President Donald Trump told US governors in a call on Monday their response to nationwide protests made them look weak and they should take a tougher stance, according to media reports.
"You have to dominate, if you don't dominate you're wasting your time. They're going to run over you, you're going to look like a bunch of jerks. You have to dominate," Trump said, according to CBS News, which cited audio it had obtained.
"You've got to arrest people, you have to track people, you have to put them in jail for 10 years and you'll never see this stuff again," he said, according to the audio.
Trump threatened to get tough himself and "activate" US Attorney General Bill Barr, CBS said. He urged governors to seek retribution, make sweeping arrests and pass laws against burning flags, CBS and the New York Times reported.