Minnesota officials say the FBI has blocked their access to an investigation into the fatal shooting of a woman by a US Immigration and Customs Enforcement (ICE) agent.

People have taken to the streets of Minneapolis to protest the killing of 37-year-old Renee Good, who died on Wednesday after being shot in her car.

Minnesota Governor Tim Walz has accused the Trump administration of blocking state officials from involvement in the case, but the US vice president said the investigation is a federal issue.

Officials have offered differing accounts of the incident, with the Trump administration claiming the ICE agent was acting in self-defence, while local officials say the woman posed no danger.

Homeland Security Secretary Kristi Noem has claimed the ICE agent shot Good multiple times because she was trying to run over the officer in her car.

The US Federal Bureau of Investigation said it would investigate the incident.

Minnesota's Bureau of Criminal Apprehension (BCA) said the FBI had initially agreed to a joint investigation with state officials but then reversed course and denied the state access to materials and evidence.

Without the ability to access all the necessary case materials and evidence, the BCA has "reluctantly withdrawn" from the investigation, the BCA's superintendent Drew Evans said in a statement.

Speaking at a news conference on Thursday, Walz said he was worried the federal government would not be able to carry out an unbiased investigation.

"It feels now that Minnesota has been taken out of the investigation," Walz said. "It feels very, very difficult that we will get a fair outcome."

Vice President JD Vance told reporters on Thursday that the investigation into the shooting was a federal issue, arguing it would go against precedent for a local official to be involved in prosecuting the case.

Videos of the incident show ICE agents approaching a car which is in the middle of the street, and tell 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 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.

At the scene of the crash on Thursday, blood from the shooting could still be seen in the snow. People set up a vigil at the site to honour Good, lining the bank with candles and roses.

Hundreds of demonstrators showed up throughout the day, shouting insults at ICE and offering their neighbours coffee on the cold winter day.

Susie Hawyard, a minister, said she went to the scene of the shooting as soon as she heard the news to verify "with my own eyes" what happened.

"I was horrified," she said. "I saw the car, I saw Renee's car, I saw Renee's blood."

Protesters also gathered at a federal building in Minneapolis early Thursday morning, where they were met with armed officers. The protests remained largely peaceful there, as residents expressed their anger over the killing of Good.

"They cannot get away with killing someone. There have to be consequences for actions," said Gavin, one of dozens of people outside the federal building.

Those who knew Good said she was a poet and guitarist who had just moved to the city of Minneapolis.

Her mother, Donna Ganger, told the Minnesota Star Tribune that her daughter was "probably terrified" during the confrontation with officers who saw her fatally shot.

"She was extremely compassionate," Ganger told the daily newspaper. "She's taken care of people all her life. She was loving, forgiving and affectionate. She was an amazing human being."

Even those who did not know Good said they were touched by her death.

"Renee was everything that was good about our community," said Nimco Ahmad, a Somali immigrant who grew up just blocks from the incident.

Ahmad said she and others were gathered to help ensure justice would be secured for Good.

The exclusion of state authorities from the probe into Good's killing is likely to undermine public trust, said Edward Maguire, a criminology professor at Arizona State University.

"From a criminological perspective, jurisdictional claims in cases like this are often less about legal requirements and more about political efforts to control the investigation and shape its outcome," he said.

But the state could still file criminal charges later against the federal officer who killed Good, said Bryna Godar, a staff attorney with the State Democracy Research Initiative at the University of Wisconsin Law School.