Chicago (AFP) - Police made at least four arrests as hundreds of protesters with the Black Lives Matter movement briefly shut stores at the sprawling Mall of America and blocked traffic at Minneapolis airport Wednesday, officials and reports said.

Separately, another eight people were arrested in a small demonstration in San Francisco, reports said, on what the activist group branded "Black Xmas."

The Minnesota mall, often described as the biggest shopping center in the US, had tried but failed to get a court order to bar the protesters -- a move activists said only strengthened their resolve to disrupt shopping on one of the biggest days in the year for retailers.

The protest, just two days before Christmas, comes with the United States embroiled in an acrimonious national debate about racism and the use of deadly force by police, particularly in their relations with black men or youths.

Black Lives Matter Minneapolis has been holding daily demonstrations to protest the fatal police shooting of Jamar Clark, 24, who they said was handcuffed when he was shot in the head on November 15.

Shops began locking up shortly before Wednesday's protest was set to begin and security guards searched the bags of people entering the mall, according to images posted on social media.

The mall issued warnings that "this demonstration is not authorized" and that "those who fail to leave the property immediately will be subject to arrest," before police in riot gear began escorting people out of the building.

Bloomington Police arrested four people over the protest, Mall of America told ABC News, although there were no reports of damage to property.

Three were arrested for trespassing and one was arrested for trespassing and disorderly conduct, ABC News said, quoting Bloomington Police.

"I'm here shopping and I'm being kicked out of #MOA," a white-haired woman who identified herself as kderong wrote on Twitter, as others posted photos of police in riot gear blocking a mall hallway.

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Television footage showed protesters chanting, "Shut it down!"

- 'Black Xmas' -

Protesters then boarded trains to the Minneapolis airport and blocked traffic by linking hands.

Black Lives Matter Minneapolis said on its Facebook page that at least 10 people were arrested during the course of the day and appealed for donations to pay their bail.

Video posted on Twitter showed the demonstrators chanting "if we don't get no justice then they don't get no peace," as snow fell on the road to the terminals.

The airport said it closed some checkpoints "to prevent protesters from gaining access to secure area," and warned travellers to give themselves extra time to make their flights.

Black Lives Matter had called for a day of action in six major US cities, including San Francisco, where eight protesters were arrested after they briefly walked onto a highway offramp by the international airport.

The demonstrators blocked traffic for about 30 minutes, the San Francisco Chronicle said.

"Black Xmas is here and there will be no business as usual until we get accountability for our dead, and justice for the living," the activist group said in a statement.

"Instead of buying gifts to fuel this system, Black Xmas is a day of action to reject the degradation of Black families and communities by police, politicians, and predatory companies, and declare our inherent worth."