The Trump administration has said it will send "hundreds more" federal officers to Minneapolis, days after the death of a woman who was shot by a US Immigration and Customs Enforcement (ICE) agent in the city.

Homeland Security Secretary Kristi Noem told Fox News that "hundreds more" will be sent to the area "in order to allow our ICE and our Border Patrol individuals that are working in Minneapolis to do so safely".

Protests against immigration enforcement have been held in cities across the US after 37-year-old Renee Nicole Good was shot in her car on Wednesday.

The Trump administration says the agent acted in self-defence. Local officials insist the woman posed no danger.

Noem said the officers will arrive "today and tomorrow" and warned action would be taken if people tried to obstruct their work.

"If they conduct violent activities against law enforcement, if they impede our operations, that's a crime, and we will hold them accountable to those consequences," she said.

Protesters gathered in Minneapolis on Saturday, with anti-ICE protests also taking place elsewhere in the US, including in Austin, Seattle, New York and Los Angeles.

Minneapolis police estimated "tens of thousands of people" attended the "ICE out of Minnesota" rally and march, which started in Powderhorn Park on Saturday.

Minneapolis Mayor Jacob Frey said the protest was "peaceful".

Police said 31 people had been arrested after protests on Friday and Saturday.

Minnesota has already seen a surge of federal law enforcement officials as the Trump administration ramps up immigration enforcement in the state.

Speaking to CNN, Noem also doubled down on her assessment that Good was committing an act of "domestic terrorism", saying she had "weaponised" her car" to attack ICE agents.

In response to her comments, Frey told CNN: "Anybody can see that this victim is not a domestic terrorist", and he said her actions were of someone trying to do a three-point turn to escape the scene.

The Minneapolis mayor added that the city's local law enforcement were "outnumbered by the number of ICE agents and beyond".

On Sunday, Minnesota senator Tina Smith, a Democrat, accused the Trump administration of trying to cover up the shooting.

"I think what we are seeing here is the federal government, Kristi Noem, Vice President Vance, Donald Trump, attempting to cover up what happened here," Smith told ABC News.

"I don't think that people here and around the country believe it," she added.

In a statement, White House spokesperson Abigail Jackson accused Smith of lying, saying: "Tina's lies only serve to further inflame tensions and incite violence against law enforcement officers."

Videos of the incident show ICE agents approaching a car which is in the middle of the street, and telling the woman behind the wheel to get out of the SUV. One of the agents tugs at the driver's side door handle.

As the vehicle attempts to drive off, one of the agents at the front of the car points their gun at the driver and several shots are heard.

The car then continues to drive away from the officer and crashes into the side of the street.

Good's wife told local media the pair had gone to the scene of immigration enforcement activity to support neighbours.

The officer who fired on Good is Jonathan Ross, a veteran ICE agent who was previously injured in the line of duty when he was struck by a car.

The FBI has said it will investigate the shooting.

On Friday, Minnesota officials said they would open their own inquiry after saying they had been frozen out of the federal investigation. Previously, US Vice-President JD Vance said the investigation is a federal issue.