Vice President Kamala Harris and former President Donald J. Trump converged on Michigan on Friday as they fought for the small pool of undecided voters and Arab Americans who could decide a battleground state that has shot toward the top of the priority list for both campaigns.

In Grand Rapids, Lansing and Oakland County, a pivotal Detroit suburb, Ms. Harris made explicit and extended overtures to blue-collar Americans as she campaigned in a state that has historically been the heart of the nation’s labor movement, and as polls show her struggling with working-class voters.

“Donald Trump is no friend of labor — let’s be really clear about that, no matter what the noise is out there,” Ms. Harris said in Grand Rapids. She promised to “work with unions to create good-paying jobs, including jobs that do not require a college degree.”

Mr. Trump hit back by promising to revitalize the auto industry through a combination of tax incentives and tariffs. As he was proclaiming at length his fondness for tariffs, his microphone cut out, leaving him visibly frustrated as he paced onstage for nearly 20 minutes.

After the technical difficulties were resolved, Mr. Trump argued that his proposals would bring an economic boom to Detroit, a city he attacked last week and whose continuing rebound he has been skeptical of. He then suggested that Ms. Harris’s tax proposals were tantamount to “economic Armageddon for Detroit.”

Throughout her speech in Grand Rapids, in Kent County, Mich. — a place Mr. Trump won in 2016 and President Biden flipped in 2020 — Ms. Harris was by turns forceful in laying out the grave stakes of the election and almost gleeful in her efforts to cast Mr. Trump as unfit for office.