A nighttime curfew was in force in Los Angeles as local officials sought to get a handle on protests that United States President Donald Trump claimed were an invasion by a “foreign enemy”.

“I have declared a local emergency and issued a curfew for central Los Angeles to stop the vandalism, to stop the looting,” Mayor Karen Bass told reporters on Tuesday.

One square mile (2.5 square kilometres) of the city’s more than 500-square-mile area will be out of bounds until 6am (13:00 GMT) for everyone apart from residents, journalists and emergency services, she added.

Small-scale and largely peaceful protests began on Friday in Los Angeles as anger swelled over intensified arrests by immigration authorities.

At their largest, a few thousand people have taken to the streets, but smaller groups have used the cover of darkness to set fires, daub graffiti and smash windows.

Overnight on Monday, 23 businesses were looted, police said, adding that more than 500 people had been arrested in recent days.

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Protests have also sprung up in other cities around the United States, including New York, Atlanta, Chicago and San Francisco.

Trump has ordered 4,000 National Guard soldiers to Los Angeles, along with 700 active-duty Marines, in what he has claimed is a necessary escalation to take back control, despite the insistence of local law enforcement that they could handle matters.

The Pentagon said the deployment would cost US taxpayers $134m.

“What you are witnessing in California is a full-blown assault on peace, on public order, and national sovereignty,” Trump told troops at Fort Bragg, a military base in North Carolina.

“This anarchy will not stand. We will not allow an American city to be invaded and conquered by a foreign enemy.”

California Governor Gavin Newsom said Trump’s shock militarisation of the city was the behaviour of “a tyrant, not a president”.

In a livestreamed address, Newsom called Trump a “president who wants to be bound by no law or constitution, perpetuating a unified assault on American tradition”.

“California may be first, but it clearly will not end here.”

In a filing to the US District Court in Northern California, Newsom asked for an injunction preventing the use of troops for policing.

Trump’s use of the military is an “incredibly rare” move for a US president, said Rachel VanLandingham, a professor at Southwestern Law School in Los Angeles and a former US Air Force lieutenant colonel.

US law largely prevents the use of the military as a policing force – absent the declaration of an insurrection, which Trump again mused about on Tuesday.

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Trump “is trying to use emergency declarations to justify bringing in first the National Guard and then mobilising Marines,” said law professor Frank Bowman of the University of Missouri.