Former President Donald J. Trump leads his closest rival by double digits in a poll of likely Iowa caucusgoers released Monday, a showing that demonstrates both his continued political dominance and the remarkable stability of the Republican race.

The survey, conducted by The Des Moines Register, NBC News and Mediacom before and after Mr. Trump’s latest indictment in Georgia, found that 42 percent of Republican voters in the state planned to support Mr. Trump, who held a lead of 23 percentage points over Gov. Ron DeSantis of Florida, with 19 percent support. In third place was Senator Tim Scott of South Carolina, with 9 percent.

The findings, which come as Mr. Trump’s rivals have poured significantly more time and money into the state, were consistent with the results of a poll by The New York Times and Siena College released this month. That survey found Mr. Trump with 44 percent support among likely Iowa G.O.P. caucusgoers, Mr. DeSantis with 20 percent support and Mr. Scott with 9 percent. Other rivals who showed single-digit support in the Times/Siena poll have been unable to improve their positions, according to the poll released Monday.

The first-in-the-nation caucuses will take place on Jan. 15, 2023, the earliest nominating contest in Iowa since 2012, when it held the caucuses the first week of January. This year’s contest is seen as the best chance for Republicans to slow Mr. Trump on his way to the nomination.

Mr. Trump has turned his legal troubles into calls for support, and he recently upstaged his nearest rival, Mr. DeSantis, by showing up on the same day at the Iowa State Fair and amassing a much larger crowd.

Mr. Trump has consistently had a stronger lead in national polling. A CBS News poll conducted immediately after the Georgia indictment found him winning 62 percent of likely G.O.P. voters — the large majority of whom said his indictments had strengthened their backing. Mr. DeSantis, the second-place finisher in those results, garnered support from 16 percent of voters.

The Des Moines Register/NBC News poll of Iowa underscored the positive effect Mr. Trump’s criminal cases have had on his grip over Republicans.

The survey, conducted just before and after prosecutors in Georgia accused Mr. Trump of a criminal conspiracy to overturn the 2020 election results in the state, found that Mr. Trump had increased his lead after he faced his fourth indictment, from 38 percent support in the days before the indictment to 43 percent afterward.

The new Iowa poll offered some glimmers of hope for Mr. Trump’s nearer rivals, with likely caucusgoers indicating an openness to Mr. DeSantis, Mr. Scott and Nikki Haley, a former United Nations ambassador and governor of South Carolina.

Mr. DeSantis had the highest favorability rating among likely Republican caucusgoers of any candidate, including Mr. Trump. Sixty-six percent of respondents said they held favorable opinions of the Florida governor, compared with 65 percent of voters who viewed Mr. Trump favorably, a difference that fell within the poll’s margin of error.

In the poll, Ms. Haley and former Vice President Mike Pence both had 6 percent support. Former Gov. Chris Christie of New Jersey was at 5 percent, the entrepreneur Vivek Ramaswamy at 4 percent and Gov. Doug Burgum of North Dakota at 2 percent.

All of those candidates have qualified for the first Republican National Committee debate on Wednesday, which Mr. Trump has signaled he will not join because of his commanding polling lead. No other candidates received support above 2 percent.

The Iowa poll found that a majority of respondents — 52 percent — said they could “still be persuaded to support a different candidate,” while 40 percent said their minds were “made up.”

Mr. Trump’s support was primarily made up of the latter group of voters, with two-thirds of his backers saying they would stick by him. Among Mr. DeSantis’s supporters, however, less than a third said their minds were made up.

Mr. Trump led by more than 20 percentage points over Mr. DeSantis among self-identified Republicans, first-time caucusgoers and evangelicals, according to the poll. But Mr. DeSantis performed better with independents than Mr. Trump, with 52 percent viewing Mr. DeSantis favorably compared with 44 percent for Mr. Trump.

Still, Mr. Trump and Mr. DeSantis remained closely matched on one metric: the “Iowa footprint,” which adds up for each candidate those who listed that candidate as their first choice, their second choice and those who said they were “actively considering” that candidate.

By that measure, Mr. DeSantis was two percentage points away from Mr. Trump at 61 percent, versus Mr. Trump’s 63 percent. Mr. Scott and Ms. Haley followed with 53 percent and 40 percent.