Gov. Chris Sununu of New Hampshire, a Republican, surprised his party on Tuesday by announcing he would not run for U.S. Senate next year, rejecting a full-court press from national Republicans who tried to recruit him to compete for a Democratic-held seat that the G.O.P. believed could determine control of the Senate.

Instead, Mr. Sununu announced at a press conference, he would seek a fourth two-year term as governor, a job that he said he could make more of a difference in than in Congress, where “too often doing nothing is considered a win.”

“My responsibility is not to the gridlock and politics of Washington, it is to the citizens of New Hampshire,’’ he said.

National Republicans had seen a Sununu challenge to Senator Maggie Hassan, a Democrat, as one of their best shots to upend the Senate’s 50-50 partisan split, which gives Democrats control with the tiebreaking vote of Vice President Kamala Harris.

At a Republican gathering in Las Vegas over the weekend, where Mr. Sununu spoke, Senator Ted Cruz of Texas urged attendees to lean on Mr. Sununu, who was also mulling whether to seek re-election as governor. “Every person here needs to come up to Chris and say, ‘Governor is great but you need to run for Senate,’” Mr. Cruz said. “Because this man could single-handedly retire Chuck Schumer as majority leader of the Senate.”

Mr. Sununu, 47, was re-elected to a third two-year term in 2020 with 65 percent of the statewide vote. That was 20 percentage points better than what former President Donald J. Trump received in losing New Hampshire to President Biden. Unlike other Republican governors of blue states, such as Maryland or Massachusetts, Mr. Sununu supported Mr. Trump’s re-election, declaring at one point, “I’m a Trump guy through and through.”

A University of New Hampshire poll in September found that support for Mr. Sununu was eroding, but still high. Fifty-seven percent of New Hampshire adults approved of the job the governor was doing, including his handling of the Covid-19 pandemic. But the share of independents who approved of his performance as governor fell for the third consecutive month.