Bill Gardner, who for decades as secretary of state has fiercely defended New Hampshire’s right to hold the country’s first presidential primaries, said on Monday that he would step down after 45 years.

Mr. Gardner, a Democrat first elected in 1976, had largely enjoyed bipartisan support, even as the job of secretary of state — each state’s top elections administrator — has become more political, a national trend accelerated by former President Donald J. Trump’s false claims of widespread voting fraud.

Mr. Gardner, 73, said political reasons did not force his decision, nor was his health a factor, though he reflected during a news conference in the Statehouse in Concord on being the longest-serving secretary of state in the country — one of only four New Hampshirites to hold the job since 1929.

“The two previous secretaries of state died in office,’’ he said. “I thought about that. Was I going to be one like that?”

Asked about the future of New Hampshire’s presidential primaries, which every four years bring a wave of national attention, money and visitors, Mr. Gardner predicted other states might try to jump the line, but said the Granite State would continue to be first.

“There will be challenges,’’ he said. “They’ll find new ways to attempt it. But it should be OK.”

Among some Democrats, in particular, there is a desire to dethrone New Hampshire from its prime electoral spot, as well as Iowa with its earlier caucuses, because both states are whiter, older and more rural than the country as a whole.

An enduring obstacle is New Hampshire state law, which requires its primary to be held before any similar contest. Mr. Gardner, who held the sole power to set the primary date, had said that if another state tried to get ahead, he would simply move up New Hampshire’s date into December or even November.

Mr. Gardner escaped Mr. Trump’s campaign of personal insults and pressure in 2020, aimed at other election officials in battleground states that President Biden won, likely because the race in New Hampshire was not especially close.

However, after Mr. Trump made the baseless claim in 2016 that “millions” of illegal votes had been cast by noncitizens across the country, Mr. Gardner agreed to join a commission that Mr. Trump set up to investigate. His decision to join the commission, even after Mr. Trump falsely claimed that he had won New Hampshire, was sharply criticized by some of his fellow Democrats. The commission disbanded after numerous states refused to cooperate with what they considered to be intrusive requests for voters’ information.

Mr. Gardner defended the commission at the time, and his role on it, saying he had hoped the “facts would end up speaking for themselves” about the lack of fraud. On Monday, he reiterated his belief that the commission was meant to restore Americans’ eroding trust in election results.

But at the time, Democrats’ disappointment over his role led to the most serious challenge that he faced for re-election, in 2018, when another Democrat, Colin Van Ostern, nearly unseated Mr. Gardner.

New Hampshire’s secretary of state is elected every two years by the membership of the state legislature. Mr. Gardner’s current deputy, David Scanlan, will take over this week until the legislature holds its next election.

On Monday, praise for Mr. Gardner came from leaders of both parties.

“Secretary Gardner has fiercely defended our primary over the years, ensuring that Granite Staters play a critical role in our country’s political elections,’’ Donna Soucy, the Democratic leader of the State Senate, said in a statement.

Gov. Chris Sununu, a Republican, said that New Hampshirites “owe a tremendous debt of gratitude” to Mr. Gardner’s administration of elections that were “always open, fair, accessible and accurate.”