Representative Frank Guinta, the embattled Republican abandoned by much of his party this year, had a narrow lead in Tuesday’s New Hampshire primary.

Guinta was ahead of his challenger, Rich Ashooh, by 500 votes, with 96 percent of the precincts reporting. It’s a remarkably close reelection battle for the congressman from the First District, which includes Manchester and the southeastern part of the state.

In the aftermath of a campaign finance scandal, all of the state’s Republican establishment, including Senator Kelly Ayotte and the New Hampshire Republican Party chairwoman, Jennifer Horn, called on Guinta to resign. But he clawed his way back into contention — in part thanks to his support for Donald Trump.

If he wins, Guinta would face a difficult battle in the general election, where a recent University of New Hampshire poll showed him losing to the Democratic nominee, former representative Carol Shea-Porter, by 19 percentage points in a hypothetical matchup.

Elsewhere in the state on primary night, Ayotte easily cleared a GOP primary challenge from former state senator Jim Rubens, and in the Democratic primary for governor, party voters picked Executive Councilor Colin Van Ostern by a large margin over his opponents.

Ayotte now heads into a general election contest against Governor Maggie Hassan, a Democrat, in one of the most closely watched and consequential contests in the country. The winner of that race could determine which party controls the Senate next year.

With her large margin of victory in the primary, Ayotte quashed any speculation about GOP support for her candidacy. Ayotte has not endorsed Republican presidential candidate Donald Trump, although she has said she will vote for him. Her former primary challenger endorsed Trump and attempted to make an issue of Ayotte’s side-step on the GOP’s presidential nominee.

In an interview with WMUR-TV after being declared the primary’s winner, Ayotte thanked Rubens for a vigorous race. She said her contest with Hassan will be defined by issues other than those being defined by presidential candidates.

“I think the race will be defined by who can best deliver results for the people of New Hampshire,’’ Ayotte said.

Hassan did not face a Democratic primary challenger.

In the race to succeed Hassan as governor, Van Ostern defeated former Portsmouth mayor Steve Marchand and former state securities director Mark Connolly in the Democratic primary.

The race in the GOP primary for governor remained too close to determine a winner, with Executive Councilor Chris Sununu, a son of a former governor and a brother of a former senator, and state Representative Frank Edelblut leading the pack of candidates.

If Sununu wins the primary, the 41-year-old will face Van Ostern, 37, and New Hampshire will have its youngest governor in 63 years.

An Edelblut victory would come as a shock to many Republicans in the state who viewed him as a widely unknown candidate.

In the Second Congressional District, which includes Concord and the western part of New Hampshire, former state representative Jim Lawrence won the GOP primary, making him the first African-American to be nominated by either party for major office in state history.

Lawrence defeated state Representative Jack Flanagan, and he will now challenge two-term Representative Annie Kuster.

The newly minted GOP nominee will have an uphill battle against Kuster. Not only has the district been trending toward Democrats in recent elections, but Kuster also has a $2 million campaign cash advantage.

Both Shea-Porter and Kuster ran unopposed in their Democratic primaries for the First and Second Districts, respectively.

Material from the Associated Press was included in this report. James Pindell can be reached at james.pindell@ globe.com. Follow him on Twitter @jamespindell or subscribe to his daily e-mail update on the 2016 campaign at www.bostonglobe.com/ groundgame.