Democratic US Senator Amy Klobuchar has said she is running for governor in her home state of Minnesota amid the tumult of an ongoing immigration crackdown.

In a video released on Thursday, she called for unity across all parties, billing herself as someone who could heal political divisions and was "willing to find common ground".

Her candidacy comes after the incumbent governor, Tim Walz, announced he would end his re-election campaign early amid criticism of his handling of a fraud scandal in the state.

Klobuchar, a four-term senator, reportedly delayed her announcement after federal agents fatally shot Alex Pretti on Saturday, two weeks after they also killed another US citizen, Renee Good.

These killings and other altercations have put the tactics and use of force by federal agents under intense scrutiny.