Senator Amy Klobuchar of Minnesota formally announced her campaign for governor on Thursday with a call for unity and decency in her troubled state, which has been roiled by political violence, President Trump’s immigration crackdown and widespread protests after two killings of Minnesotans by federal agents.

Ms. Klobuchar, a popular Democrat with a history of winning by double-digit margins, has spent nearly two decades in the Senate as a common-sense centrist with a folksy demeanor and a carefully cultivated history of bipartisanship.

Now, with her run for governor, the self-proclaimed “senator next door” is gambling that her message of moving past partisan divides can still work even amid one of the most volatile domestic conflicts of the second Trump administration.