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George E. Pataki, the former three-term New York governor who undertook a long-shot presidential bid that failed to catch fire, withdrew from the presidential race on Tuesday, urging Republicans in a televised message to nominate another candidate who could bring the country together.

In a two-minute advertisement that aired on NBC affiliates in Iowa, New Hampshire and South Carolina, Mr. Pataki, seated before a flickering fire, announced he was suspending his campaign.

The next president must unite the country, Mr. Pataki said, “If we’re truly going to make America great again,” an allusion to the campaign slogan of Donald J. Trump, who Mr. Pataki has often criticized.

His withdrawal from the race leaves 12 Republican candidates still in the field at the battle heads toward its first contest, the Iowa caucuses, which are just a month away.

Mr. Pataki announced his campaign in May, urging Republicans in a New Hampshire speech to court a racially diverse array of voters with a message of economic opportunity.

His wife, Libby, described him then as a candidate who would appeal to Republican moderates, and Mr. Pataki concentrated his efforts on New Hampshire, where independent voters hold powerful sway.

But the mild-mannered former Peekskill, N.Y., mayor appeared from the start to be an awkward match for the fired-up Republican base of 2016. A supporter of abortion rights and environmental conservation, Mr. Pataki always faced the narrowest of paths to his party’s nomination.

Mr. Pataki was one of the earliest and most persistent critics of Mr. Trump, but his own brand of blue-state Republicanism failed to secure him a distinctive space in a crowded presidential field. He struggled to raise money and watched as Republican governors of more recent vintage, led by Chris Christie of New Jersey, outflanked him in New Hampshire.

Earle I. Mack, a prominent real estate developer and Republican donor who was supporting Mr. Pataki, said the former governor had faced a difficult national environment for his “middle of the road” brand of politics. Mr. Mack, who spoke with Mr. Pataki ahead of his announcement, said Republicans faced a dire future if they did not tack toward the center, as Mr. Pataki had urged.

“It’s time for a more moderate Republican,” Mr. Mack said, adding: “If we don’t have a candidate that understands the Supreme Court has ruled that gay marriage is legal and a woman’s right to choose is legal, if they can’t get that through their head, they’re going to keep losing elections.”

Dave Currier, a former New Hampshire state senator who was supporting Mr. Pataki, said the former governor had described his decision as a matter of resources: with money low and few campaign staff, Mr. Currier said the Pataki effort “didn’t have the resources here to really put it together.”

Because of Mr. Pataki’s limited support in the race, it is unclear what impact his withdrawal might have on the rest of the candidates.

But Mr. Currier said he had already received phone calls about the campaign Tuesday evening from four other camps, including Mr. Trump’s. A longtime admirer of Mr. Pataki, Mr. Currier said he was most intrigued by Mr. Christie and Senator Marco Rubio of Florida.

Yet Mr. Pataki, he said, would be tough to replace in the field.

“He’s very knowledgable, he’s a very bright guy and I don’t see that in a lot of these other candidates,” Mr. Currier said.

In selling his bid to voters, Mr. Pataki often harkened back to achievements from more than a decade earlier, such as his role helping New York recover from the Sept. 11, 2001 terror attacks, and his upset victory in 1994 over Mario M. Cuomo, the legendary liberal Democrat who governed New York for three terms.

Even his more hawkish foreign policy message failed to set Mr. Pataki apart from a collection of candidates who have grown increasingly strident in their calls for military action against the Islamic State group in Syria.

Who Is Running for President? Donald J. Trump officially accepted the Republican party’s nomination on July 22. Hillary Clinton was officially nominated on July 26 at the Democratic Convention.