The former Republican governor of Maryland, Larry Hogan, a fierce critic of President Trump, said Sunday he will not run for the White House in 2024, after long positioning himself as a possible alternative to the former president.

Mr. Hogan, 66, wrote in The New York Times that while he appreciated “all those around the nation who have for many years encouraged me to run for president, after eight years of pouring my heart and soul into serving the people of Maryland, I have no desire to put my family through another grueling campaign just for the experience.”

Mr. Hogan wrapped up his second term in January, serving for eight years in a state where Democrats outnumber Republicans by a 2-to-1 margin. He was Maryland’s second Republican governor ever to be reelected.

Some Republicans had hoped that Mr. Hogan, emerging as the new best hope of a small group of “Never Trump Republicans,” would challenge Mr. Trump in 2020. But a year after Mr. Hogan’s reelection in 2018, he said that while he appreciated “all of the encouragement” he had received to run for president, he would not. Mr. Hogan told The Associated Press he had no interest in a “kamikaze mission.”

Mr. Hogan has acknowledged he would be an underdog in the 2024 GOP presidential primary. But he also noted that he had been considered a long shot to become governor in a heavily Democratic state.

After Mr. Trump’s former United Nations ambassador, Nikki Haley, announced her White House campaign in February, Mr. Hogan said he would “absolutely” consider sitting out the 2024 race if it appeared that Mr. Trump could benefit from a large field of rivals who could splinter support among non-Trump candidates.

“That would be a pretty good reason to consider not running, absolutely,” Mr. Hogan said on NBC’s “Meet the Press.”

In the past two presidential elections, Mr. Hogan said he did not vote for Mr. Trump, the party nominee. Mr. Hogan said he wrote in the name of his father, former congressman Larry Hogan Sr., in 2016 and the late President Reagan in 2020.

Mr. Hogan won his first term as governor in 2014 in an upset, using public campaign financing against a better-funded candidate. Running on fiscal concerns as a moderate Republican businessman, Mr. Hogan tapped into frustration from a variety of tax and fee increases over the eight previous years to defeat then-Lieutenant Governor Anthony Brown. Mr. Hogan had never held elected office before.

Politics also ran in the Hogan family: Mr. Hogan’s father was the only Republican to vote for all three articles of impeachment against President Nixon on the House Judiciary Committee.

In his first year as governor, Mr. Hogan went right to work on pocketbook issues. He lowered tolls, an action he could take without approval from the General Assembly, long controlled by Democrats. He was also presented with challenges, however, including unrest in Baltimore following the death of Freddie Gray in police custody in 2015. Mr. Hogan sent the National Guard to prevent further rioting.

In June of that year, he was diagnosed with stage 3 non-Hodgkin’s lymphoma but continued working while receiving treatment. He has been in remission since November 2015.

In 2018, he became only the second Republican governor in the history of the state to win reelection, defeating former NAACP President Ben Jealous.

While Mr. Hogan liked to promote bipartisan cooperation with Democrats when he could, he had no shortage of disagreements with the legislature, particularly on high-profile issues. Democratic supermajorities were able to override Mr. Hogan’s vetoes, especially on priority measures such as a sweeping and expensive education funding overhaul, three policing measures and legislation to expand abortion access in the state.

Mr. Hogan won a long-sought victory last year by getting tax relief for retirees. And after Mr. Hogan’s long criticism of the state’s congressional and state legislative maps for gerrymandering, a Maryland judge struck down the congressional lines last year that had been drawn by Democrats. The map was redrawn, resulting in a much more competitive district in the western part of the state.

Mr. Hogan has long been upfront about his distaste for Mr. Trump as president.

In 2020, as chair of the National Governors Association, Mr. Hogan criticized Mr. Trump for delaying a national coronavirus testing strategy, saying the president was playing down the virus’ threat despite grave warnings from top national experts.

“I did not go out of my way to criticize the president,” Mr. Hogan said. “But unlike a lot of Republicans, I’m not the guy that’s just going to sit down and shut up and not stand up and say something if I think something’s going wrong.”

Describing the riot at the U.S. Capitol on January 6, 2021, as “one of the darkest days in American history,” Mr. Hogan said Mr. Trump should have resigned or been removed from office.

“The people that try to whitewash January 6 as if nothing happened are delusional. It was an assault on democracy,” Mr. Hogan told the AP late last year.

Messrs. Trump and Hogan were engaged in a proxy battle of sorts in the 2022 election. Mr. Hogan’s pick for governor was Kelly Schulz, who was labor secretary and commerce secretary in his administration. She lost in the Republican primary to Trump-endorsed Dan Cox, a state lawmaker who said President Biden’s 2020 victory shouldn’t have been certified and who sought to impeach Mr. Hogan for his pandemic policies.

Mr. Cox went on to lose the November general election by a large margin to Democrat Wes Moore.

In November, two weeks after Trump announced his 2024 campaign, Mr. Hogan launched his own political action committee, saying “the party and the country needs to move on” from Mr. Trump and acknowledging the speculation about his own political future.

“I know there is no shortage of naysayers, but I’ve always been an underdog, and people have always counted us out, but every single time, we’ve beaten the odds,” Mr. Hogan added.