President Biden is promoting his four-year efforts to support labor unions and rural communities in the upper Midwest as his chief deputy, Vice President Kamala Harris, looks for a sweep of “blue wall” states to win the White House.

Mr. Biden stopped in swing-state Michigan on Friday, a day after visiting battleground Wisconsin, another key prize, to support union workers at a pipe-fitting training center in Ann Arbor.

The president contrasted his signature infrastructure law with former President Donald Trump’s inability to deliver similar legislation, part of a pattern of increasing attacks on his predecessor.

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“He never built a damn thing, not one thing. Not a joke —not one,” Mr. Biden said.  “Do you think he has any idea what [union workers] do? I’m not being a wise guy. I mean, all he did was lose his father’s money.”

Mr. Biden said, “Kamala and I,” by contrast, ensured more than $10 billion for projects in Michigan through his signature infrastructure legislation.

The president also said that inflation would ease again in the next monthly report. Inflation was 2.9% in July, having dropped steadily from a four-decade high of 9.1% in June 2022.

“I predict it is going to come down a little more,” Mr. Biden said.

Rising costs are a key sore spot for his administration and Ms. Harris’s bid but the president, who dropped his reelection campaign in July, got a warm reception in Michigan.

During the event, Mr. Biden signed a “Good Jobs” executive order that directs agencies to emphasize family-sustaining wages, workplace safety and a fair opportunity to join a union.

“Thank you Joe! Thank you Joe!” the crowd shouted as Mr. Biden took the stage.

Mr. Biden is on an “Investing in America” tour highlighting his efforts to lift the economy through policies known as “Bidenomics.”

The tour allows the president to promote his tenure while serving as a tacit way to promote Ms. Harris’s presidential bid against Mr. Trump, the GOP nominee.

Mr. Biden left the race amid questions about his age and fitness for office, meaning he will likely be deployed selectively on behalf of his replacement.

Yet he’s conducting some efforts on his own aimed at benefitting both his legacy and his preferred successor. So far, his efforts have been directed toward blue-collar workers and rural residents in swing states.

He appeared with Ms. Harris in Pittsburgh on Labor Day before holding an official White House event in Westby, Wisconsin, on Thursday to promote new funding for rural electricity projects.

Michigan is a major prize in the November election. It will award 15 electoral votes.

Mr. Trump won Michigan by a whisker in 2016 before Mr. Biden swiped it back for Democrats in 2020.

Polling averages show Ms. Harris has a slight lead over Mr. Trump, though the race in the state is considered statistically tied.

One recent poll from WDIV/Detroit News showed Mr. Trump narrowly leading Ms. Harris in the state, 44.7% to 43.5%.

Michigan is home to a large Arab-American population that might sour on Ms. Harris over the Biden administration’s support for Israel during the war in Gaza.

Michigan is part of an upper Midwest trio of states that Ms. Harris hopes to turn into a “blue wall” in November.

Her running mate, Minnesota Gov. Tim Walz, leads one of them and both presidential nominees are making stops in Wisconsin, with Mr. Trump holding a rally in Mosinee on Saturday.

While Ms. Harris and Mr. Walz are positioning themselves as champions of union labor, Mr. Trump is courting the auto industry by criticizing electric-vehicle mandates from the Biden-Harris administration.

Mr. Trump says allowing Americans to choose the vehicle of their liking will help Michigan’s auto sector remain competitive with overseas makers.

On Thursday, Mr. Trump said he would enact tariffs to bolster the auto industry and fight to reduce the corporate tax rate “solely” for companies that make their products in the U.S. to 15% from 21%.

On Friday, a person in the crowd shouted “Bull—” when Mr. Biden discussed his predecessor’s level of commitment to products Made in America.

“Well, you said it better than I can,” Mr. Biden responded.

• Seth McLaughlin contributed to this report.