Geico has made a rare leadership change and accelerated its advertising spending as the company and its little green lizard climb the ranks of the nation’s largest auto insurers.

Warren Buffett’s Berkshire Hathaway, which owns the Chevy Chase-based insurance company, last week elevated Bill Roberts to president and chief operating officer at Geico. Roberts is stepping up from the role of executive vice president, in which he has focused on marketing, advertising and online business, all areas in which the company has excelled in recent years.

“Bill will take on a greater role in managing Geico’s day-to-day operations,” Tony Nicely, who previously served as president and will continue to serve as chairman and chief executive, said in a statement.

Nicely, who has spent more than a half-century at Geico, said that he “will continue to be very actively involved in the overall management of the company” but that he “could not be more confident that Bill is ready to tackle these new responsibilities.”

The leadership shuffle comes as the company closes in on Allstate as the nation’s second-largest auto insurer. The industry leader is State Farm.

Geico surpassed Allstate in business during the first quarter of the year, posting $4.72 billion in new auto insurance premiums, compared with its competitor’s $4.53 billion. Allstate, though, has picked up more business over four quarters, $17.65 billion in premiums to Geico’s $17.16 billion, according to data released late last month by SNL Financial, a provider of business information.

Geico executives rely on annual data from A.M. Best when referring to their standing in the market, and the latest report from A.M. Best still had the company in third place. The company would not comment on its movement in the rankings — but others have.

“After years of consistent premium growth, Geico is in position to become the second largest U.S. personal auto writer in 2013,” SNL analysts Raisa Luis and Terry Leone wrote in a research report.

Competitors are taking notice. A couple of years ago, Allstate purchased online auto insurer ­Esurance for about $1 billion, aiming to recapture some of the market share it was losing to smaller rivals, including Buffett’s company.

“We acquired Esurance so that we could really compete effectively against Geico and Progressive in that customer segment,” Allstate chief executive Don Civgin told analysts during a quarterly earnings call in February.

On the same day as Geico’s leadership announcement, the company reported that it had sold its 12 millionth car policy. (The firm now covers more than 18 million total vehicles.) Meanwhile, the company’s underwriting profit jumped 18 percent last year and its employee rolls have grown to 28,000, about 5,000 of whom are based in the Washington area.

Continued investments in the company’s familiar gecko mascot and several new advertising campaigns — featuring an array of cavemen, a talking pig and folk singers — have fueled some of that growth.

In 2012, Geico spent more than $1.1 billion on advertising, up 12.45 percent from the year before and an even greater boost than the 10.1 percent increase its posted between 2010 and 2011, SNL’s data show. A company representative declined to answer questions about advertising spending.

It was by far the most spent by any property insurer last year — Allstate was a distant second, at $828.8 million — and the fifth-largest amount spent on advertising by any company in the United States, according to data Ad Age planned to publish Monday.

Geico’s multimedia campaigns now represent a “vast majority” of the advertising budget at Berkshire Hathaway.

Buffett highlighted Geico’s overall success and that of its marketing campaigns in a letter to shareholders in March, noting that the firm’s share of the auto market has surged to 9.7 percent from 2.5 percent when he took control in 1995.

“The credit for Geico’s extraordinary performance goes to Tony Nicely and his 27,000 associates,” Buffett wrote. “And to that cast, we should add our Gecko. Neither rain nor storm nor gloom of night can stop him; the little lizard just soldiers on”