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HIGHLAND HILLS, Ohio — Hillary Clinton began the final sprint to Tuesday’s nominating contests in five states with a visit to church here on Sunday. She had spent the previous few days apologizing for wrongly saying that Nancy Reagan had “started a national conversation” about HIV/AIDS during the administration of her husband, President Ronald Reagan.

At the Mount Zion Fellowship, a predominantly African-American church outside Cleveland, Mrs. Clinton stressed her resilience to congregants on Sunday by sharing a favorite saying of Eleanor Roosevelt.

“A woman is like a tea bag,” Mrs. Clinton said. “You don’t know how strong she is until she gets into hot water.”

The church’s followers represented a key constituency for Mrs. Clinton as she seeks to shore up support among minority voters ahead of Tuesday’s contests, hoping her strength among African-Americans can counter inroads Senator Bernie Sanders has made with young voters and working-class whites.

Clinton aides predict tight races in the Midwestern states where economically struggling voters have gravitated to the populist pitch of Mr. Sanders. But even if she loses in the Rust Belt, they see tremendous upside in Florida and North Carolina, where black, Latino and older voters are expected on Tuesday to give Mrs. Clinton a healthy edge in the race for delegates.

“Even if he won in Ohio, Michigan, Illinois,” Robby Mook, Mrs. Clinton’s campaign manager, said. “We would still have more delegates on the 15th because of their performance in delegate-rich Florida and North Carolina.”

On Monday, Mrs. Clinton will campaign in Chicago and Springfield, Ill., followed by a get-out-the-vote rally in Charlotte, N.C.

As Mr. Sanders runs ads attacking Mrs. Clinton’s positions on global trade deals that many voters blame for widespread job losses, Mrs. Clinton has emphasized her proposals to bring jobs back to the United States and has criticized Mr. Sanders for not presenting specific plans to do the same.

Speaking to a crowd of about 500 people at M7 Technologies, a factory in Youngstown, Ohio, on Saturday night, Mrs. Clinton vowed to end steel dumping by China and other nations, a factor that had hit the economy in the state’s Mahoning Valley area.

“I have always been committed to bringing back manufacturing,” she said. “And I’m the only candidate, on either side, who actually has a plan to do that.”

On Sunday afternoon, Mrs. Clinton stopped in at the 8 Sisters Bakery in Marion, Ohio. “I really want to have a conversation,” she told a dozen potential voters seated at wooden tables near a display of pastries.

“I’m very interested in hearing from each of you about your lives,” Mrs. Clinton said. “What you think is working, your challenges, how the economy is going or not going, what needs to be done to create more opportunities in Marion and around it.”