President Trump’s campaign is moving to head off Ambassador Nikki Haley in New Hampshire as the state emerges as the most likely venue for a candidate to muster a real challenge to the former president, in a primary election increasingly dominated by Mr. Trump.

Nationwide, Mr. Trump’s support among GOP voters has only grown. FiveThirtyEight’s polling average shows that support for Mr. Trump in the GOP primary has risen to about 63 percent from about 53 percent six months ago.

At New Hampshire, though, a recent poll from CBS News and YouGov suggests that Ms. Haley is within 15 points of the former president, trailing him 29 percent to 44 percent in the field.

While FiveThirtyEight’s average is less favorable to Ms. Haley, showing her trailing Mr. Trump 19 percent to 44 percent, she is closer to the former president at New Hampshire than Governor DeSantis is in Iowa, where he trails Mr. Trump 20 percent to 50 percent.

Although a 15-point lead would be a landslide victory in most elections, in this Republican primary, Ms. Haley is coming closer to challenging Mr. Trump in New Hampshire than any candidate has come since early 2023, when it appeared Mr. DeSantis might be able to credibly challenge him.

In response to Ms. Haley’s relatively favorable polling in the Granite State, a super PAC supporting Mr. Trump has launched a new ad campaign against Ms. Haley there.

The ad, which first aired early Tuesday, attacks Ms. Haley for apparently changing her position on a gas tax between 2013 and 2015, fashioning the former ambassador as “Nikki ‘high tax’ Haley.”

The ad, bought by MAGA Inc., is the first that Mr. Trump’s supporters have placed against another candidate in New Hampshire since June, and it may demonstrate that the former president wants to lock down the nomination by ensuring wins in Iowa and New Hampshire, according to a political scientist at John Jay College, Brian Arbour.

“His campaign is taking winning New Hampshire pretty seriously,” Mr. Arbour tells the Sun. “Of course, if they can win Iowa and win New Hampshire, I’m not sure anything else matters.”

Mr. Arbour explains that New Hampshire is an outlier state in the GOP primary because relatively few evangelical voters reside there, and primaries there are often decided by which candidate can get the most backing from independent voters.

“In a party that has become so socially conservative focused, New Hampshire has relatively few evangelical voters and a much more libertarian- and/or business-oriented bent to its conservatism,” Mr. Arbour said.

Mr. Haley has responded to the Trump ad in a tweet, saying that it shows, “Someone’s getting nervous.”

“Two days ago, Donald Trump denied our surge in New Hampshire existed,” Ms. Haley said. “Now, he’s running a negative ad against me.”

Ms. Haley’s campaign did not immediately respond to a Sun request for comment.

In a tweet Tuesday, a MAGA Inc. spokeswoman, Karoline Leavitt, said that the group “remains committed to exposing the career politicians who are undeserving of the Republican nomination.”

“Nikki Haley has lied to increase taxes, she has lied to get in the race, and she will try to lie to win it,” Ms. Leavitt said. “We won’t let another tax-and-spend politician try to fool the voters.”

While Mr. Arbour did give credence to the idea that New Hampshire seems like the most likely early state for a surprise upset, he also cautioned that the prospect looks unlikely.

“Republican voters like Trump and there’s no indication a large portion want to or will turn against him,” Mr. Arbour said. “Until we see that the story of this race doesn’t change.”

He added that Mr. Trump looks poised to win Iowa, New Hampshire, and South Carolina, saying, “We’re in the general election by March 1.”