A lawyer for the family of George Floyd, whose death sparked unrest across the US, has accused a police officer of "premeditated murder".
Minneapolis policeman Derek Chauvin has been charged with third-degree murder, but lawyer Benjamin Crump told CBS news it was a case of first-degree murder.
"We think that he had intent... almost nine minutes he kept his knee in a man's neck that was begging and pleading for breath," he said.
Looting is reported in Philadelphia.
Video from two Philadelphia TV stations on Sunday shows youths smashing several police cars and looting at least one store.
Reporting on the violence in West Philadelphia, the Philadelphia Inquirer says police cars were also set ablaze.
Several US cities have imposed curfews.
President Donald Trump tweeted: "Law & Order in Philadelphia, NOW! They are looting stores. Call in our great National Guard".
The Floyd case in Minneapolis has reignited US anger over police killings of black Americans.
It follows the high-profile cases of Michael Brown in Ferguson, Eric Garner in New York and others that have driven the Black Lives Matter movement.
In video footage, Mr Chauvin, 44, can be seen kneeling on Mr Floyd's neck for several minutes on Monday. Mr Floyd, 46, repeatedly says that he is unable to breathe.
"The fact that officer Chauvin kept his knee on his neck for almost three minutes after he was unconscious. We don't understand how that was not first degree murder. We don't understand how all these officers haven't been arrested," lawyer Crump said.
Three other officers present at the time have also since been sacked.
For many the outrage over George Floyd's death also reflects years of frustration over socio-economic inequality and segregation, not least in Minneapolis itself.
There have been five nights of arson and looting in Minneapolis and the adjacent city of St Paul. Minnesota's Governor Tim Walz said on Saturday he was deploying the full Minnesota National Guard for the first time since World War Two.
Governor Walz said racism in his state had created the conditions for Mr Floyd's death.
The National Guard - the US reserve military force for domestic emergencies - said on Sunday that 5,000 of its personnel had been activated in 15 states and Washington DC. It added that "state and local law enforcement agencies remain responsible for security".
In the CBS interview, lawyer Benjamin Crump also said "we now have the audio from the police bodycam and we hear where one officer says 'he doesn't have a pulse, maybe we should turn him on his side', but yet officer Chauvin says 'no, we're going to keep him in this position'. That's intent.
"Also, the fact that officer Chauvin kept his knee on his neck for almost three minutes after he was unconscious."
The lawyer also said Mr Chauvin and Mr Floyd already knew each other before Mr Floyd's death in custody.
He said the Floyd family was "notified by the owner of a club that Derek Chauvin was an off-duty police officer where George Floyd was a security guard, and so they had to overlap".
For three years, Donald Trump presided over a nation of relative peace and prosperity. The crises he faced were largely of his own making, and he confronted them by rallying his supporters and condemning his opponents.
Now Trump faces a situation ill-suited to a playbook of division. The US economy has been hobbled by a deadly pandemic. George Floyd's death at the hands of a Minneapolis police officer has spread racial unrest across the nation. The public is uncertain and afraid - and increasingly angry.
These are circumstances that would test the abilities of even the most skilful leaders. This president, however, risks becoming lost at sea. His public calls for unity and healing have been undermined by a penchant for Twitter name-calling and bellicosity. Message discipline, a valuable attribute at this moment, is not his forte.
There may be no easy way to guide the nation through its current peril. Barack Obama's measured coolness did nothing to stop the fires of Ferguson any more than Richard Nixon's law-and-order edicts quelled Vietnam-era unrest.
The economic and social devastation of the pandemic has created a political landscape of dry brush ignited by the lightning strike of Floyd's death. The president may not be able to contain the wildfire, even if he isn't feeding the flames.
What's the latest on the protests?
Huge demonstrations have taken place in at least 30 cities across the US. They were largely peaceful on Saturday, but violence flared later in the day.
Besides Minneapolis and Los Angeles, the cities under night curfew include Atlanta, Chicago, Denver, Louisville, Richmond, San Francisco and Seattle.
One of the cities worst affected by unrest is Los Angeles. California Governor Gavin Newsom declared a state of emergency in the city and activated the National Guard.
The entire city is under curfew. Numerous shops have been looted, including on the famous retail avenues, Melrose and Fairfax, while overhead footage showed fires burning. Earlier police fired rubber bullets and hit protesters with batons. Hundreds of arrests have been made.
In New York City, police arrested about 350 people overnight and dozens of police suffered light injuries.
In Salt Lake City, a man aimed a bow and arrow at protesters and was attacked by the crowd, Reuters reported.
President Trump's national security adviser told CNN "I don't think there's systemic racism" in the police.
Robert O'Brien said "there are some racist police, I think they're the minority, I think they're the few bad apples and we need to root them out".
On Saturday evening, President Trump said Mr Floyd's death had "filled Americans with horror, anger and grief".
He also denounced the actions of "looters and anarchists", accusing them of dishonouring the memory of Mr Floyd. What was needed, he said, was "healing not hatred, justice not chaos". "I will not allow angry mobs to dominate - won't happen," he added.
Thousands took part in an anti-racism protest march in central London on Sunday, defying social distancing rules imposed because of coronavirus. They gathered in Trafalgar Square, then the crowd moved on to the US embassy.