More than four in 10 voters, regardless of party affiliation, said they believed Mrs. Clinton was not very religious, according to a Pew Research Center study on “Faith and the 2016 Campaign” released in January. Among Democrats and voters who lean toward the Democratic Party, about two-thirds said Mrs. Clinton was at least “somewhat” religious; 27 percent said she was not.

But amid the political mudslinging with Mr. Trump — and a stubbornly high number of voters who dislike and distrust her — Mrs. Clinton must show voters more of herself and explain her own motivations, aides said.

“We believe we have to work extra hard to make sure the positive notion she wants to do breaks through given the amount of interest there is in what he says,” said Jennifer Palmieri, a spokeswoman for the Clinton campaign.

The speech on Thursday was the first of several in which Mrs. Clinton will try to connect her personal motivations with policies. In the coming weeks, she will give at least three addresses, about the economy, proposals to help children and families and a call to national service.

She sought to reinforce her deep roots in African-American churches on Thursday, paying tribute to several of the Baptist congregations she had visited during the campaign, and present herself as the antithesis of Mr. Trump, who drew criticism last week after revelations that his campaign had prewritten questions and responses when he spoke at a black church.

“I’m sure you’re sick and tired of politicians who think they can just show up at election time, say a few nice words and earn your support,” said Mrs. Clinton, whose relationship with the group stretches back decades.

Mr. Trump has accused Mrs. Clinton of “bigotry” toward African-Americans and said she and other Democrats had pandered to black voters without helping them find jobs and reduce crime.