WASHINGTON — Senator Rob Portman of Ohio, a Republican with deep ties to the former party establishment, announced on Monday that he would not seek re-election in 2022, underscoring the rightward shift of his party and opening a major battleground in what will be a bruising national fight for Senate control.

One of the most seasoned legislators in the Senate, Mr. Portman, 65, voiced frustration with the deep polarization and partisanship in Washington as one of the factors in his decision to step aside after a successful career in the House, executive branch and Senate.

“It has gotten harder and harder to break through the partisan gridlock and mark progress on substantive policy, and that has contributed to my decision,” Mr. Portman said in a statement that was widely viewed as a surprise so soon after the last election.

Mr. Portman, a top trade and budget official in the administration of George W. Bush, was once regarded as a conservative stalwart. But as his party shifted to the right in recent years, he had come to be seen as one of the few right-of-center Republican senators interested in striking bipartisan deals, an increasingly perilous enterprise at a time when the party’s core supporters have shown a penchant for punishing moderation.

Mr. Portman was one of the lawmakers responsible for pushing through the new North American trade deal in 2019. He was also part of a bipartisan coalition that crafted a pandemic relief measure late last year and applied pressure to the House and Senate leadership to embrace and pass it after months of delay.

With the Senate increasingly a gridlocked battlefield, Mr. Portman is the latest Republican to assess the political landscape and opt for an exit, putting seats in play in competitive states. Senators Richard M. Burr of North Carolina and Patrick J. Toomey of Pennsylvania have announced they will not be running again. Former President Donald J. Trump won Ohio soundly, but he only narrowly prevailed in North Carolina and was defeated in Pennsylvania.

Mr. Portman is highly regarded by members of both parties.

“Rob and I haven’t always agreed with one another,” Senator Sherrod Brown, Mr. Portman’s Democratic counterpart in Ohio, wrote on Twitter. “But we’ve always been able to put our differences aside to do what’s best for Ohio.”

Mr. Portman sought to maneuver carefully around Mr. Trump while he was in office, carefully criticizing the former president’s actions and statements he disagreed with while praising Mr. Trump’s policies. He voted against removing Mr. Trump from office in the Senate impeachment trial last year, and is considered unlikely to convict the former president in the forthcoming one, even though he will not face voters again.

The senator’s decision to retire rather than seek a third term illustrated how difficult it has become for more mainstream Republicans to navigate the current political environment, with hard-right allies of Mr. Trump insisting that Republican members of Congress side with them or face primary contests.

Mr. Portman called it a “tough time to be in public service.”

“We live in an increasingly polarized country where members of both parties are being pushed further to the right and further to the left,” he said, “and that means too few people who are actively looking to find common ground.”

With the Senate split 50-50 and Democrats in the majority by virtue of Vice President Kamala Harris breaking any ties, Republicans would need a net gain of one seat to take back the majority they lost this month after six years in control.

Given the Republican tilt of Ohio, which supported Mr. Trump in the presidential election, Republicans would hold the advantage in the race, particularly in a midterm election where the party out of presidential power typically fares well. But the open seat could make it easier for Democrats to compete, particularly if Republicans choose a hard-right candidate with the potential to alienate independents and suburban voters.

One of those hard-right prospects, Representative Jim Jordan of Ohio, was among the first names mentioned on Monday as a possible replacement for Mr. Portman. Perhaps Mr. Trump’s staunchest ally in the House, Mr. Jordan was the former president’s principal defender on the House floor when Mr. Trump was impeached for a second time this month.

Mr. Jordan’s frequent Fox News appearances have also earned him national fame with conservatives; he had over $5 million left over when his 2020 campaign ended.

Yet his profile has also made Mr. Jordan a political lightning rod, and a number of Ohio Democrats believe he would be the easiest Republican to defeat. If he did enter the race, he would likely have company in the primary. Representative Steve Stivers, a Columbus-area lawmaker and the former chairman of the House campaign committee, indicated to associates on Monday that he was considering a bid. Other potential Republicans included Lt. Gov. Jon Husted; Jane Timken, the chairwoman of the state party; and Representatives Bill Johnson and Michael R. Turner.

The roster of potential Democratic candidates is smaller in what has become a Republican-dominated state. The two most formidable candidates could be Mayor Nan Whaley of Dayton and Representative Tim Ryan. Ms. Whaley has been expected to run for governor, but when asked on Monday if she would enter the Senate contest, she said she was “thinking about it.”

Mr. Ryan, who represents a heavily industrial slice of northeastern Ohio, has repeatedly mulled statewide campaigns, only to run for re-election. He did, however, mount a long-shot presidential campaign in 2019 and has made little secret of his angst in the House, having once tried to dethrone Speaker Nancy Pelosi. Mr. Ryan may have another good reason to finally run statewide: After he won by a smaller-than-expected margin last year, Ohio Republicans could carve up his seat in redistricting to make it hard for him to win.

Whoever emerges for the Democrats will confront a state that has shifted sharply to the right after decades as the country’s quintessential political battleground. Mr. Brown is the last statewide Democratic officeholder, having won re-election against lackluster opposition in 2018.

Mr. Portman said he made his plans public on Monday to give others time to prepare for a costly statewide race. His advisers said that besides his unhappiness with the partisanship of Washington, he was wary of making an eight-year commitment that would keep him in the Senate into his 70s.