The US state of Minnesota has sued the Trump administration to block a surge of federal immigration agents into the state.

The lawsuit argues the deployment amounts to an unconstitutional "federal invasion".

Minnesota's Attorney General Keith Ellison said immigration operations had upended life for millions and caused "chaos and violence".

It comes after Renee Good, 37, was shot dead by an immigration agent in Minneapolis last week, triggering large protests in the city.

The lawsuit asks a federal court to declare the deployment illegal. The Trump administration has described the legal action as "baseless".

It has said that the agents are targeting undocumented migrants, and further agents are needed to ensure their safety during operations.

In a news conference on Monday, Ellison said the deployment violated the state's "sovereign authority to protect the health and well-being of every single person who lives within our borders.

Minneapolis Mayor Jacob Frey alleged that agents were illegally targeting people whom they assumed to be immigrants based on racial profiling.

He said their actions had led to an increase in 911 calls and forced city police to work overtime investigating incidents involving Immigration and Customs Enforcement (ICE).

"The unlawful deployment of thousands of armed, masked, and poorly trained federal agents is hurting Minnesota," Ellison said.

He accused the Trump administration of "persecuting the state of Minnesota because of our political views". Democrats currently hold the governorship and control the state legislature.

"Keith Ellison made it abundantly clear today he is prioritising politics over public safety," Tricia McLaughlin from the Department of Homeland Security said in a statement.

"This is a baseless lawsuit, and we look forward to proving that in court."

During the news conference, prosecutors said they would seek a temporary restraining order to block the deployment as early as Tuesday.

It comes as the US Department of Homeland Security says it plans to send more agents into the state as part of its Operation Metro Surge.

The department says the deployment is necessary to combat illegal immigration and crime. According to recent estimates, around 2,000 agents have been deployed to Minnesota.

Over the weekend, 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".

The state of Illinois and the city of Chicago filed a similar lawsuit on Monday against what it called an "organised bombardment" and "occupation" by federal immigration agents.

"Uniformed, military-trained personnel, carrying semi-automatic firearms and military-grade weaponry, have rampaged for months through Chicago and the surrounding areas," the Illinois lawsuit states.

The shooting of Good last week led to a fierce debate over federal law enforcement operations in US cities.

Federal officials allege that the 37-year-old was attempting to run over immigration agents with her car when she was shot. Local officials have disputed this, and say firing shots was not necessary.

The FBI has said it will investigate the shooting. Local officials say they are being shut out of the federal investigation.