US President Donald Trump has said the fatal shooting of a woman by an Immigration and Customs Enforcement agent in Minneapolis appeared to be an act of self-defence, as local and state officials disputed the federal account and called for an investigation.

Posting on Truth Social, Trump said the woman driving a vehicle had "violently, wilfully, and viciously ran over the ICE Officer," adding that the agent "seems to have shot her in self-defence."

Federal authorities said the incident occurred during an enforcement operation on Wednesday.

The Department of Homeland Security said the woman, identified as a 37-year-old, attempted to strike officers with her vehicle, prompting an agent to open fire.

An ICE agent "acted quickly and defensively," Homeland Security Secretary Kristi Noem said, adding that the woman was struck and later died.

However, Minneapolis Mayor Jacob Frey rejected that account, saying he had reviewed video footage of the incident and did not believe the shooting was justified.

He called the use of force reckless and demanded that federal immigration agents leave the city.

"We’re demanding ICE to leave the city immediately. We stand rock solid with our immigrant and refugee communities," Frey said.

Minnesota Governor Tim Walz echoed the mayor’s concerns, warning the public against what he called the "propaganda machine" of the Department of Homeland Security.

He said the state would ensure a "full, fair, and expeditious investigation."

Walz also said he had issued a warning order to prepare the Minnesota National Guard for possible deployment.