Thousands of demonstrators chanting the name of the woman killed by a federal agent in Minneapolis took to the city's streets on Saturday, amid widespread anger at use of force in the Trump administration's immigration crackdown.

Organisers said more than 1,000 events were planned across the US under the slogan "ICE, Out for Good" -- referring to the Immigration and Customs Enforcement agency that is drawing growing opposition over its execution of President Donald Trump's effort at mass deportations.

The slogan is also a reference to Renee Good, the 37-year-old mother shot dead in her car by an ICE agent in the midwestern US city of Minneapolis on Wednesday.

Thousands braved frigid weather and streamed toward a snow-covered park to mobilise near the scene of the shooting.

They carried signs demanding "ICE OUT" of Minnesota.

At the start of the protest, a voice called out, "Say her name!" The crowd shouted back: "Renee Good!"

Her death has sparked strong emotions in this Democratic stronghold, and further afield.

In Philadelphia, protesters marched in the rain from City Hall to the ICE field office.

Others mobilised in New York, Washington and Boston.

More protests were planned for Sunday.

The calls to protest were being amplified by the "No Kings" movement, a network of left-wing organisations that mounted nationwide demonstrations against Trump last year.

The Trump administration has sought to paint Good as a "domestic terrorist," insisting the agent who fatally shot her was acting in self-defence.

This narrative is strongly disputed by local officials, who say footage shows Good's vehicle was turning away from the agent and did not pose a threat.

Cell phone footage apparently taken by the officer who fired the fatal shots shows him interacting with Good, who had blocked the road with her car in an apparent effort to impede the agents.

He approaches and circles Good's car, as she says to him: "I'm not mad at you."

After he passes in front of the car, another agent can be heard ordering Good to exit the vehicle before she tries to drive off and shots ring out.

The agent filming the video can be heard making derogatory comments about the woman at the end of the clip.

The White House insisted the video gave weight to the officer's claim of self-defence -- even though the clip does not show the moment the car moved away, or him opening fire.

Drew Lenzmeier, 30, said he joined the protest in Minneapolis "because I feel our rights are being taken away from us and we are turning into an authoritarian dictatorship."

"No one is stopping the Trump administration from now murdering citizens and stealing, kidnapping human beings. It's time to stop," he said.

On Friday evening, hundreds gathered noisily in front of Minneapolis hotels believed to be housing ICE agents, equipped with whistles, loudspeakers and musical instruments.

Several people were arrested and then quickly released, according to police.

Officials and residents in Minnesota have expressed concern that local law enforcement agencies have been shut out of the FBI investigation into Minneapolis shooting.

According to The Trace, a media outlet focusing on gun violence, Good was the fourth person killed by federal immigration agents since the launch of the Trump administration's deportation campaign.

Seven people have been injured.

In a separate incident, two people were injured Thursday in Portland, Oregon, by shots fired by federal border police during a traffic stop. (AFP)