WASHINGTON — Roy Blunt of Missouri, the No. 4 Senate Republican, announced on Monday that he would not seek re-election in 2022, the latest in a string of party veterans who have opted to exit Congress as the G.O.P. remakes itself in the mold of former President Donald J. Trump.

Mr. Blunt, a fixture of the Republican establishment, had told reporters in January that he was planning to run for a third term and had taken steps to avoid alienating the former president. But with his surprise announcement on Monday, he joined a growing group of institutionalists who have chosen to leave rather than potentially subject themselves to party primaries that promise to be contests of which candidate can tie himself more closely to Mr. Trump.

“After 14 general election victories — three to county office, seven to the United States House of Representatives and four statewide elections — I won’t be a candidate for re-election to the United States Senate next year,” Mr. Blunt, 71, said in a two-minute video posted on social media.

Speaking later to reporters in Springfield, Mo., Mr. Blunt predicted he would have won Mr. Trump’s endorsement and prevailed if he had run again, but said he did not want to commit to another eight years of campaigning and service in Congress.

“I felt good about getting elected, but what I felt less good about was whether I wanted to go from 26 years in the Congress to 32 years in the Congress and maybe eliminate the other things I might get a chance to do,” he said.

Republicans are confident they can hold his seat in a state that has swung hard to the right over the last decade. Still, Mr. Blunt’s departure adds to a brain drain already underway among Senate Republicans.

A bipartisan deal maker and stalwart of Washington social circles known for well-tailored suits and disarming charm, he is the rare figure who has served in high-ranking posts in both House and Senate leadership. Mr. Blunt was also in charge of planning President Biden’s inauguration in January, a delicate task that required him to navigate explosive political crosscurrents and the threat of violence after the Jan. 6 mob attack on the Capitol.

His decision not to seek another term follows similar ones by Senator Rob Portman of Ohio, one of Republicans’ leading policy minds and a seeker of bipartisan compromises; Senator Richard C. Shelby of Alabama, a deal-making former chairman of the Appropriations Committee; and Senator Patrick J. Toomey of Pennsylvania, a top party voice on free-market economics. Republicans are still closely watching Senator Charles E. Grassley of Iowa, 87, their longest-serving member, to see if he will seek another term.

In their place has emerged a crop of Trump acolytes who have mirrored the former president’s combative style, shunned compromise with Democrats and so far been more willing to buck Senator Mitch McConnell of Kentucky, the long-serving top Republican leader with whom Mr. Blunt closely allied himself.

“There are two kinds of politicians in Washington — those who want to make a point, and those who want to make a difference. Senator Blunt always worked to make a difference,” said Antonia Ferrier, a former longtime Republican aide who worked for Mr. Blunt in the House and later for Mr. McConnell. “There is no question that his departure, on top of those like Senators Alexander and Shelby, leaves a hole of those who know how to forge bipartisan legislative deals.”

In a fawning statement, Mr. McConnell called Mr. Blunt a “policy heavyweight” who had helped bring home legislative victories for Republicans and the Senate as a whole. Among Mr. Blunt’s proudest were billions of dollars in new funding he helped secure as an appropriator for medical research, including for cancer, Alzheimer’s disease and mental health. He was also a savvy political tactician who was talked about both as a possible successor to Mr. McConnell and as a sought-after negotiating partner for Democrats.

Those qualities, once prized in government, have slowly become political liabilities among Republican primary voters whose loyalty to Mr. Trump and distrust of official Washington have reshaped the party. Mr. Blunt had not formally drawn a primary challenger, but his close alliance with Mr. McConnell, who has openly sought to purge Mr. Trump from the party, and his status as a consummate Washington insider put him at risk.

Eric Greitens, a Republican who resigned as Missouri’s governor in a cloud of scandal in 2018, said last week that he was “evaluating” whether to challenge Mr. Blunt in a primary. Mr. Greitens, a decorated member of the Navy SEALs, has sought to position himself as an heir to Mr. Trump and accused Mr. Blunt of inadequately backing him.

“It’s not enough to have an ‘R’ behind their name. We have to have people who are willing to take on the establishment to actually fight against the swamp,” Mr. Greitens told a St. Louis radio station.

Mr. Blunt had only occasionally criticized Mr. Trump during his four years in office, careful not to anger the former president who helped him secure a narrow victory in 2016.

The Capitol riot proved a more difficult path to walk. Afterward, Mr. Blunt broke with most of Missouri’s Republican delegation and voted to confirm Mr. Biden’s election victory after the attack. He called Mr. Trump’s actions “clearly reckless” and said Jan. 6 had been “a sad and terrible day in the history of the country.” But he vocally opposed Mr. Trump’s impeachment.

Mr. Blunt had no cross words for either Mr. Trump or Mr. Greitens on Monday, but he warned against the ascendant brand of politics in his party focused not on solving problems for people but on drawing lines in the sand and picking fights.

“The country in the last decade or so has sort of fallen off the edge of too many politicians saying, ‘If you’ll vote for me, I’ll never compromise on anything,’” he told reporters in Springfield. “That is a philosophy that particularly does not work in a democracy.”

Among other Republicans considering running for the seat are Jay Ashcroft, the Missouri secretary of state; Eric Schmitt, the attorney general; Jean Evans, a former state party leader; Mike Kehoe, the lieutenant governor; Representatives Jason Smith and Ann Wagner; and Carl Edwards, a former NASCAR driver.

With Republicans’ newfound dominance in Missouri, statewide contests have increasingly been decided in G.O.P. primaries. But John Hancock, a former state party chairman, warned that there was always a risk that so many ambitious young Republicans vying for the nomination could lead to a “divisive primary” backfiring.

“There are benefits and detriments to having a deep bench,” he said.

Democrats, who have lost nearly every race for statewide office over the last decade, have no clear front-runner at the moment.

Scott Sifton, a veteran of the Missouri statehouse, has already jumped into the race and put together a full campaign team. Democrats in the state have suggested one of its two Democratic members of Congress, Cori Bush of St. Louis and Emanuel Cleaver II of Kansas City, could also run. And Quinton Lucas, the mayor of Kansas City, expressed interest on Monday.