Los Angeles mayor Karen Bass issued a curfew for the downtown area of her city on Tuesday in a bid to stop vandalism and looting as protests over US President Donald Trump's stepped-up enforcement of immigration laws continued in the city.

She said in a news conference that she had declared a local emergency and that the curfew will run from 8pm on Tuesday until 6am local time on Wednesday.

"We reached a tipping point" after 23 businesses were looted, Bass said.

The curfew will be in place in a 2.6 square km section of downtown that includes the area where protests have occurred since Friday.

The curfew doesn't apply to residents who live in the designated area, people who are homeless, credentialed media or public safety and emergency officials, according to Los Angeles Police Chief Jim McDonnell.

McDonnell said "unlawful and dangerous behaviour" had been escalating since Saturday.

"The curfew is a necessary measure to protect lives and safeguard property following several consecutive days of growing unrest throughout the city," McDonnell said.

Earlier on Tuesday, National Guard troops began protecting immigration agents as they made arrests in Los Angeles on Tuesday, an expansion of their duties that had been limited to protecting federal property.

Photos posted Tuesday by US Immigration and Customs Enforcement show National Guard troops standing guard around officers as they made arrests.

ICE said in a statement that the troops were providing security at federal facilities and protecting federal officers "who are out on daily enforcement operations".

The change moves troops closer to engaging in law enforcement actions like deportations as President Donald Trump has promised as part of the administration's immigration crackdown.

California governor Gavin Newsom had asked a federal court to block the Trump administration from using the National Guard and Marines to assist with immigration raids in Los Angeles, saying it would only heighten tensions and promote civil unrest.

Newsom filed the emergency request after Trump ordered the deployment to LA of roughly 4,000 National Guard troops and 700 Marines to the city.

The federal government said Newsom was seeking an unprecedented and dangerous order that would interfere with its ability to carry out enforcement operations.

A judge set a hearing for Thursday.

The Marines and another 2,000 National Guard troops were sent to LA on Monday, adding to a military presence that local officials and Newsom do not want and that the police chief says makes it harder to handle the protests safely. (AP)