The Republican candidate for governor, John Faso, says his Democratic opponent, Eliot Spitzer, violated state lobbying rules by underpaying for flights on a private jet belonging to a casino developer who is part of a group bidding on the state racing franchise.

On May 24 and 25, Mr. Spitzer and a campaign staffer used a private jet owned by the developer, Richard Fields, to shuttle between fund-raisers in Phoenix, Tucson, Ariz., and Cincinnati. The campaign reimbursed Mr. Fields a total of $4,300 for three flights.

Mr. Faso is contending that Mr. Spitzer underreported the cost of the flights by tens of thousands of dollars and is asking the state lobbying commission to investigate the matter. The Faso campaign is accusing Mr. Spitzer of underpaying for the flights by $37,678.

In a statement, Mr. Faso said, “Mr. Spitzer has basically accepted and not reported a donation of as much as $38,000 from somebody who is currently lobbying to allow an out-of-state Indian tribe to build more casinos in New York. This is the perfect example of how Eliot Spitzer holds others to higher standards than he holds himself.”

In New York, rules governing how much lobbyists are required to charge public officials essentially follow the guidelines governing federal lawmakers, who are allowed to reimburse lobbyists for chartered flights at the cheapest available first-class commercial rates. New York lobbyists may charge the commercial fare as long as the flight originates at an airport where first-class flights are available, according to the executive director of the state lobbying commission, David Grandeau. If such first-class flights are not available, then the reimbursement rate is the price for an equivalent flight on a chartered jet.

Spitzer campaign officials say the $4,300 reimbursement is what it estimated as the cost of two tickets on three first-class flights from Phoenix to Tucson, Tucson to Cincinnati, and Cincinnati to New York City. Mr. Spitzer flew on a commercial airline to Phoenix, a spokeswoman for the Spitzer campaign, Christine Anderson, said. She did not know which airports Mr. Spitzer flew out of.

“We’re following federal law,” Ms. Anderson said.”The Spitzer campaign hasn’t done anything wrong.”

US Airways yesterday was charging a range of $5,686 to $8,360 for two tickets on first-class flights from Phoenix to Tucson to Cincinnati on Wednesday evening and a flight from Cincinnati to New York on Thursday evening, according to a US Airways agent reached by telephone. Ms. Anderson said tickets purchased further in advance would be cheaper than the price cited by the US Airways agent.

In February, the lobbying commission ruled that Mr. Spitzer’s lieutenant governor running-mate, David Paterson, a state senator from Harlem, underpaid for a ride on Mr. Fields’s jet from an airport in Westchester to Albany, a route where first-class flights are not available.

Mr. Paterson paid Mr. Fields $176 for the flight, but the commission found that he should have paid Mr. Fields $4,500. Mr. Fields paid a $9,000 fine and admitted to no wrongdoing.

The annual limit on lobbyist gifts to public officials in New York is $75.

The federal reimbursement rate for trips on private jets has come under scrutiny in the aftermath of the Jack Abramoff lobbying scandal. In January, Senator Obama of Illinois announced that he would stop taking advantage of the cheaper fare offered to lawmakers, telling the New York Times in March, “This is an example where appearances matter. Very few of my constituents have a chance to travel on a corporate jet.”

Earlier this month, Mr. Fields, a former aide to Donald Trump and the chairman of Coastal Development, became a member of Excelsior Racing Associates, one of more than a dozen groups to have placed bids to run racing at Aqueduct, Belmont Park, and Saratoga. The state Legislature and whoever is elected governor in November are expected to pick a winner next year.The New York Racing Association currently has the franchise, which expires at the end of next year.

An adviser to the state Democratic Party and Senator Clinton, Howard Wolfson, serves as a spokesman for Mr. Fields. “Richard supports Eliot Spitzer for governor for the same reason a majority of New Yorkers do: He is going to be the next governor of the state,” Mr. Wolfson said, the Associated Press reported.

The owner of the franchise will collect a percentage of the billions of dollars in bets placed at the tracks, as well as a percentage of revenue from video lottery terminals.

The Daily News last month reported that Mr. Fields hosted a fundraiser for Mr. Spitzer on July 18 at the developer’s home in Jackson Hole, Wyo. His companies donated $200,000 to the campaign before the event, the Daily News reported.

The Spitzer campaign, which had on hand more than $14 million as of July 15, has accepted thousands of dollars from contributors involved with other franchise bidders.