She also portrayed herself as a candidate who could attract independent, undecided and even Republican voters unhappy with Mr. Trump’s campaign. “I want to say something to people who may be reconsidering their support of my opponent,” she said. “I know you still may have questions for me, I respect that. I want to answer them. I want to earn your vote.”

Her stop here marked the start of a rare multiday tour of swing states as the Clinton campaign revved up its efforts to decisively defeat Mr. Trump on Nov. 8, including releasing a powerful minute-long ad featuring Khizr Khan, the father of a Muslim American soldier killed in Iraq. The ad featuring Mr. Khan, who was attacked by Mr. Trump after he spoke at the Democratic convention, will run in Ohio, Florida, Pennsylvania and North Carolina, as well as other crucial states.

With Mrs. Clinton holding a healthy lead in most national polls, Democrats have turned their focus to trying to ensure victory by as large a margin as possible, deploying Michelle Obama in Arizona and President Obama in Florida. The larger the victory, the less Mr. Trump and his supporters can claim foul play, Mrs. Clinton’s allies said.

A month ago, Ohio seemed to be aligning as a Trump stronghold, as its large bloc of white working-class voters responded to Mr. Trump’s economic populism and America-first message. But the state is now back in play, with a poll from Suffolk University in Boston showing a tied race.

Mrs. Clinton’s afternoon rally at a community college in Cleveland, the heart of Democratic strength in Ohio, was aimed at increasing early voting, which began last week.