Molly Kelly Wins in New Hampshire and Will Face Sununu for Governor’s Seat

“I’m going to run on the issues that are most important to the people of New Hampshire,’’ she added, “and make it clear that there are real differences between Chris Sununu and myself.”

Mr. Pappas calls himself a progressive, but he does not lean as far left as the label has come to imply during this election cycle. He has said he supports universal health care, but not Medicare for All, now one of the hallmarks of left-wing progressivism.

In an interview last month, he said he was in favor of immigration reform, but did not go as far as to call for abolishing the Immigration and Customs Enforcement agency, another item on some progressive agendas. And he declined to say whether he would support Representative Nancy Pelosi for speaker if Democrats win control of the House.

“The leadership should clearly reflect the diversity of the Democratic caucus, and so we’ll sort that all out once the election is over,” he said in the interview.

Mr. Pappas and Mr. Edwards will compete to succeed Representative Carol Shea-Porter, a Democrat, who is retiring. President Trump carried the district, in the Eastern half of the state, by two points in 2016, and Republicans see it as a potential target this fall, though election experts expect the seat to stay in Democratic hands.

If Mr. Pappas’s primary victory did not come as a surprise, given the backing he received from the local Democratic establishment, he had to contend with a strong opponent in a race that grew increasingly heated. In the final days before the primary, he and Ms. Sullivan traded barbs, with Mr. Pappas’s campaign attacking Ms. Sullivan for not voting in the 2016 presidential primary and Ms. Sullivan questioning Mr. Pappas’s progressive record.

Ms. Sullivan enjoyed some national support, raising nearly $2 million through mid-August, but her tenuous connection to the state — she had been considered a possible House candidate in Illinois, her home state, before moving here last year — was viewed as potentially problematic.