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Without the ability to access all the necessary case materials and evidence, the BCA has reluctantly withdrawn from the investigation, the BCA's superintendent Drew Evans said in a statement.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

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.

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

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.

Those who knew Good said she was a poet and guitarist who had just moved to the city of Minneapolis. Her mother, Donna Ganger, remarked that her daughter was likely terrified during the confrontation with the officers that led to her being fatally shot.

The exclusion of state authorities from the probe into Good's killing is likely to undermine public trust. However, the state could still file criminal charges later against the federal officer who killed Good.