Gov. Ron DeSantis of Florida paused, looked down and then told a banquet hall filled with conservative Iowa Christians something that he had never before said in public: His wife, Casey DeSantis, experienced a miscarriage several years ago during her first pregnancy.

The couple, Mr. DeSantis explained on Friday at a forum for Republican presidential candidates hosted by an influential evangelical group, had been trying to conceive before taking a trip to Israel.

“We went to Ruth’s tomb in Hebron — Ruth, Chapter 4, Verse 13 — and we prayed,” Mr. DeSantis, citing Scripture, said at the event in Des Moines. “We prayed a lot to have a family, and then, lo and behold, we go back to the United States and a little time later we got pregnant. But unfortunately we lost that first baby.”

The deeply personal revelation — in response to a question about the importance of the nuclear family — was an unexpected moment for Mr. DeSantis, who is usually tight-lipped about both his faith and his family life. On the campaign trail, he rotates through a limited set of anecdotes about Ms. DeSantis and their three young children, as well as his religious beliefs. Still, at the Iowa event, he lingered only briefly on his wife’s miscarriage, calling it simply a “tough thing” and a test of faith.

Mr. DeSantis, a Roman Catholic, is heavily courting Iowa’s religious right, which has helped deliver the state’s last three competitive Republican presidential caucuses to candidates who wore their faith on their sleeves. White evangelical voters are likely to play a decisive role in the state’s Jan. 15 caucuses, the first contest in the 2024 G.O.P. primary, and they often turn to politicians who speak the language of the church.

“You have to talk authentically from the heart,” said Terry Amann, a conservative pastor from Des Moines. “Anybody can cite Bible verses.”

If Mr. DeSantis has any hope of beating former President Donald J. Trump, the front-runner, who leads him by roughly 30 points in Iowa polls, it lies in winning over conservative Christian voters while fending off the challenge of Nikki Haley, the former governor of South Carolina, who is seen as more moderate.

A DeSantis victory in Iowa remains a long shot, but Mr. Trump’s criticisms of the hard-line abortion restrictions favored by many evangelical voters in Iowa may have created a lane for the Florida governor to bolster his standing. The former president has described a six-week abortion ban signed by Mr. DeSantis in Florida as “a terrible mistake.” Mr. Trump has blamed extreme positions on abortion for recent Republican losses at the polls and, looking to win over moderates in the general election, has avoided supporting a federal abortion ban. That has deeply disappointed some evangelical leaders and voters who cheered him after his appointments to the Supreme Court helped overturn Roe v. Wade.

“Trump has backed off his pro-life position,” said Mike Demastus, who leads an evangelical church in Des Moines. “And that’s caused voters like myself to pause and be willing to listen to other candidates.”

Mr. DeSantis is trying to take advantage of concerns like Mr. Demastus’s. As he opened his new Iowa campaign headquarters outside Des Moines on Saturday, the governor told reporters that Mr. Trump’s comments on abortion had been the real “mistake.” He had previously said of Mr. Trump, during an interview with an Iowa radio station, that “all pro-lifers should know that he’s preparing to sell you out.”

Still, Mr. Trump remains immensely popular with conservative Christians, and not only because of his role in Roe’s demise. Mr. Trump moved the United States Embassy in Israel from Tel Aviv to Jerusalem, an issue of deep importance to many evangelicals. He is also credited for his anti-immigration policies and for a strong economy during his presidency, reflecting the fact that many religious voters have political concerns beyond their faith.

Even many of the evangelical voters who support Mr. DeSantis are deeply grateful to the former president.

“The reversal of Roe v. Wade — I didn’t ever think that would happen in my lifetime, and he did that,” Jerry Buseman, 54, a retired school administrator from Hampton, Iowa, said of Mr. Trump.

Now, the DeSantis and Trump campaigns are engaged in a back-and-forth to win over faith leaders and voters. Evangelicals are the single largest religious group among Iowa Republicans, accounting for more than a third of their ranks, according to Pew Research Center. So far, polls suggest Mr. Trump is winning the race for their votes. The former president had the support of 51 percent of white evangelical voters, compared with 30 percent for Mr. DeSantis, according to a September poll by CBS News and YouGov. It’s a major shift from 2016, when evangelicals flocked to Ted Cruz rather than to Mr. Trump, helping the Republican senator from Texas win the caucuses that year.

“Trump has already proven himself to have a backbone,” said Brad Sherman, a pastor and state legislator who has endorsed Mr. Trump, even though he said he wished the former president would take a “stronger stand” against abortion. “He’s shown that he will do what he says.”

Like Mr. Sherman, many Iowans backing Mr. Trump seem willing to forgive his more recent comments on abortion. Only 40 percent of Trump supporters agreed that he was right to criticize six-week abortion bans, according to an October poll by The Des Moines Register, NBC News and Mediacom.

Alex Latcham, the Trump campaign’s early-states director, said the former president had gotten results on issues that had been “the top priorities” for evangelical voters for decades. In his Des Moines office, Mr. Latcham said, he keeps a map of Iowa showing the locations of more than 100 religious leaders who have endorsed Mr. Trump.

“There’s plenty of time, but right now it’s Trump’s to lose,” said Steve Scheffler, the president of the Iowa Faith and Freedom Coalition, who is staying neutral through the caucuses.

To counter Mr. Trump’s popularity, Mr. DeSantis held his first official campaign rally in May at a church outside Des Moines, where a group of pastors prayed over him. He has rolled out his own endorsements from more than 100 religious leaders around the state. Before each Republican presidential debate, he has invited a pastor to pray for him and his wife in the green room backstage. His campaign holds a monthly video call for pastors. And unlike Mr. Trump, he has attended several church services in Iowa, including alongside the Iowa evangelical leader Bob Vander Plaats, who hosted Mr. DeSantis at the forum where he discussed his wife’s miscarriage.

Never Back Down, a super PAC supporting the DeSantis campaign, has produced advertisements that accuse Mr. Trump of a “betrayal of the pro-life movement,” call into question his support for Israel and criticize his attacks on Kim Reynolds, the popular Iowa governor who has endorsed Mr. DeSantis and has also signed a six-week abortion ban.

”DeSantis has done an outstanding job networking with evangelicals,” said David Kochel, a veteran Iowa political strategist. “He’s running the campaign the right way. The problem is he’s doing it against someone who has already delivered for evangelical voters.”

Ms. Haley, the other top runner-up in the race, who is now tied with Mr. DeSantis in many Iowa polls, does not appear to be pursuing the state’s faith leaders as aggressively, and her more measured way of talking about abortion has turned off many evangelicals.

Olivia Perez-Cubas, a spokeswoman for the Haley campaign, highlighted Ms. Haley’s “steadfast support for Israel” as a reason for evangelical voters to get behind her. And she pointed to Ms. Haley’s recent endorsement by Marlys Popma, a prominent anti-abortion activist in Iowa.

For Mr. DeSantis, a lack of folksy charm may still be an issue in Iowa, despite his efforts to be more personal with evangelical voters.

Evangelical voters “want to see the heart,” said Sam Brownback, a conservative Christian and former Republican senator from Kansas whose own presidential campaign failed to take off in 2008. “They want to see what you really are inside.”

The last three Republicans to win contested caucuses — former Gov. Mike Huckabee of Arkansas, former Senator Rick Santorum of Pennsylvania and Mr. Cruz — all talked easily about their faith. (None of them captured the nomination.)

Mr. DeSantis, who has been criticized as stilted on the campaign trail, is not built in that mold. Instead, he is relying on his record as Florida governor, which includes, in addition to the six-week abortion ban, laws to restrict the rights of transgender people and to limit discussions of sexuality in schools.

When a reporter asked why he was a better fit for Iowa’s evangelicals than Mr. Trump — a thrice-married former Democrat — Mr. DeSantis replied that he was “better representative of their values.”

“I have a better record of actually delivering on my promises and fighting important fights on behalf of children, on behalf of families and on behalf of religious liberty,” he said on Saturday at a coffee shop in Ottumwa, Iowa.

Heidi Sokol, 51, a Republican voter who teaches at a Christian school in Clear Lake, Iowa, said she wasn’t bothered that Mr. DeSantis spoke far more about policy than about his personal faith when she saw him speak at a Des Moines church this fall.

“We’re not hiring the president to be our pastor,” Ms. Sokol said.

Ruth Igielnik contributed reporting from Washington, D.C.; Ann Hinga Klein from Ottumwa; and Chris Cameron from Newton, Iowa.