A popular GOP governor has declined to run for Senate, delivering a potential setback to Republicans’ chances of taking control of the 50-50 chamber in next year’s midterms.

New Hampshire Gov. Chris Sununu said Tuesday he won’t challenge incumbent Sen. Maggie Hassan for her seat. Republicans had said Mr. Sununu, who has governed as a centrist, was one of their best hopes to win a Democrat-held seat if he ran.

Mr....

A popular GOP governor has declined to run for Senate, delivering a potential setback to Republicans’ chances of taking control of the 50-50 chamber in next year’s midterms.

New Hampshire Gov. Chris Sununu said Tuesday he won’t challenge incumbent Sen. Maggie Hassan for her seat. Republicans had said Mr. Sununu, who has governed as a centrist, was one of their best hopes to win a Democrat-held seat if he ran.

Mr. Sununu said he would instead run for a fourth term as governor.

“We have a lot more to do to protect the interests of New Hampshire citizens, and it’s just clear I can be the most effective doing that here in the corner office in the Granite State,” he said. “I haven’t ruled out going to Washington, just not as a senator right now.”

The Senate is currently evenly split between Democrats and Republicans, but Democrats have control as Vice President Kamala Harris can act as a tiebreaking vote.

“This idea that I’m the 51st vote in the U.S. Senate that would get rid of Chuck Schumer, I frankly think Republicans stand to win 53, 54 seats in the U.S. Senate, including New Hampshire and it’s not just Chris Sununu that can win that race,” Mr. Sununu told reporters. Mr. Schumer, a New York Democrat, is the current majority leader.

“We know that no matter who emerges as the Republican nominee, this is going to be a hard-fought race,” said Aaron Jacobs, Ms. Hassan’s campaign manager. “The senator has shown that she can work across the aisle to get results for Granite Staters—and that is why she has a record of winning tough races.”

Mr. Sununu, who supported former President Donald Trump but has rejected his false claims of election fraud, said he didn’t warn Minority Leader Mitch McConnell (R., Ky.) or the chairman of the Republican Senate campaign arm before his announcement Tuesday. Mr. Trump, Mr. McConnell and Florida Sen. Rick Scott had been public about their desire for Mr. Sununu to get in the race. The GOP leader has also failed to recruit Arizona’s popular GOP governor for that state’s Senate seat.

“Maggie Hassan is the least popular and most vulnerable incumbent in the U.S. Senate, and for good reason. She’s done nothing but defend Joe Biden’s

failed agenda and embrace the policies of the radical left,” said National Republican Senatorial Committee spokesman Chris Hartline.

A representative for Mr. McConnell declined to comment.

Sen. Maggie Hassan, the former two-term governor in New Hampshire, won her seat in 2016 by just over 1,000 votes.

Photo: Tom Williams/Zuma Press

A handful of competitive races, including in New Hampshire, will decide which party will control the chamber in 2023. Thirty-four Senate seats are up for re-election in 2022, but only nine are currently considered competitive, according to nonpartisan election watcher Cook Political Report.

Ms. Hassan, the former two-term governor in New Hampshire, won her seat in 2016 by just over 1,000 votes. The state is seen as a true battleground: It has two Democratic senators and two Democratic House members but a Republican governor and GOP majorities in the state legislature.

President Biden won the state by 7 percentage points in 2020, but his poll numbers have plummeted in recent months.

A St. Anselm poll of the state released late last month had Mr. Sununu up 5 percentage points over Ms. Hassan in a prospective matchup. The poll of 1,323 registered voters had a margin or error of plus or minus 2.7 points.

Retired Brig. Gen. Donald Bolduc, who ran unsuccessfully for the GOP Senate nomination in 2020, is running again. He has positioned himself to the right of Mr. Sununu.

Write to Eliza Collins at eliza.collins+1@wsj.com.