Mr. DeSantis’s first visit to Iowa included stops at Rhythm City Casino Resort in Davenport and the Elwell Family Food Center, a large event space at the Iowa State Fairgrounds. Curiosity about the rising Republican star helped draw healthy crowds: On a snowy, chilly weekday, more than 1,000 people had arrived at the casino by 9 a.m. and a similar standing-room-only crowd was on hand at 5 p.m. in Des Moines.

“I liked that he was down to earth,” Rob Corry, a 57-year-old real estate consultant, said after getting his book signed at the state fairgrounds, where, as in Davenport, free copies were passed out to the audience. “He didn’t go for any wild and crazy applause lines and just let his record speak for itself. We don’t need a big show in Iowa.”

Still, Mr. DeSantis seems determined to keep an arm’s-length distance as he introduces himself to voters, and his Iowa events showcased both his strengths and his weaknesses.

He’s at his best standing in front of a camera armed with studied talking points. In Davenport, he spent more than 30 minutes at a podium, paging through notes as he relived a re-election victory with a record-breaking margin and recalled his efforts to block Covid-19 vaccine mandates in his state.

Waving his hands and pointing at the crowd to make his points, Mr. DeSantis drew applause at least 10 times during the first 10 minutes of his speech, including for his victory in Miami-Dade County, which, he pointed out, Hillary Clinton won in 2016 by about 30 points.

Ms. Clinton’s opponent that year was Mr. Trump, but Mr. DeSantis never mentioned his party leader’s name. His potential rival for the Republican nomination has scheduled his own event in Davenport for Monday.

Instead, Mr. DeSantis drew clear contrasts by focusing on his victory in the state — which came amid major disappointments for Republicans at the national level, losses that have been largely blamed on Mr. Trump.