“What does the Sermon on the Mount really mean?” Mrs. Clinton said, referring to the sermon in which the eight Beatitudes are outlined by Jesus Christ, including “Blessed are the meek.” “It sure does seem to favor the poor and the merciful, and those who in worldly terms don’t have a lot, but who have the spirit that God recognizes as the core of love and salvation.”

For all the efforts her campaign has made to reintroduce Mrs. Clinton over the past eight months, her religiousness remains little-known. 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 on Wednesday. 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.

Though Republican candidates aggressively court evangelicals, who make up a particularly powerful conservative constituency in Iowa, Democrats — whose voters are a more diverse lot, in sectarian terms — tend to be more cautious in talking about religion. (Mrs. Clinton’s main opponent, Senator Bernie Sanders, who is Jewish, has said he is “not particularly religious.”)

But for Mrs. Clinton, a candidate who struggles with questions of authenticity, her evident ease at discussing her faith and Scripture — and how they help explain why she is running for president — might well help her connect not just to the faithful but to nonreligious voters as well.

“It doesn’t reach the bulk of Democratic voters,” said Mike McCurry, a former White House press secretary to Bill Clinton who is now a professor of public theology at Wesley Theological Seminary. “But in Hillary’s case, what you want to hear is about character and values and what motivates her.”

On Wednesday, during a quick fund-raising trip to Philadelphia, Mrs. Clinton spoke with 50 African-American pastors at Mother Bethel African Methodist Episcopal Church, in what she called a “stimulating and inspirational meeting.” The same night, Mr. Clinton told a crowd in Mason City, Iowa, that “if you really want to understand Hillary, you just have to understand” she was raised a Methodist, and mentioned one of her favorite spirituals: “If I Could Help Somebody.”

“I won’t bore you with all the verses,” Mrs. Clinton said, “but the last line is, ‘If I can help somebody when I travel along, then my living will not be in vain.’”