Fairfax County Board Chairman John F. Herrity, after meeting with D.C. Mayor Marion Barry at the mayor's office yesterday morning, announced that he had offered to help the city obtain private financing to build a new football stadium in the District.

Herrity's offer was the latest in a series of developments since Washington Redskins owner Jack Kent Cooke said last month that he wants a 75,000-seat, domed arena to replace Robert F. Kennedy Stadium, which seats 55,000.

Cooke said RFK is too small and has said he may take the team to the suburbs if his demands are not met.

"Our primary mission is to keep the Redskins in the metropolitan area," Herrity said after the meeting, which lasted about 45 minutes.

"We feel that the District ought to be the place of first choice."

If that effort is unsuccessful, Herrity said, "Obviously, there would be some interest in terms of Fairfax or other areas of the region."

A Washington Post poll of 1,146 registered voters in Fairfax shows that a majority in the county, 72 percent, opposes the idea of building a football stadium with taxpayers' money.

But more than half of those polled, 55 percent, said they would like a football stadium as long as taxpayers did not have to pay for it.

District officials have vowed to keep the Redskins in the city.

Barry last week suggested several possibilities for financing a new stadium, including a "one-time" federal grant or a "regional cooperative venture."

Barry said he would hire consultants to explore the feasibility of various options.

Yesterday's meeting, while far from producing a concrete proposal, was the first time officials have publicly raised the idea of assembling private investors in partnership with the city government.

Given the reluctance of Congress to commit money to large public projects, the possibility of federal financing for a new stadium is considered remote.

Nor have suburban elected officials leaped to endorse the idea of contributing public money to a project that essentially benefits the District of Columbia.

Among surrounding counties, only Prince William is making a concerted bid for the Redskins.

According to a source, Cooke called the county this week to express his interest in Prince William and to request a meeting with county officials.

The source said a date has not yet been set.

Montgomery County officials have said they would be happy to talk with Cooke, but have ruled out public financing.

Prince George's officials have taken a similar position.

Appearing alongside Herrity at a brief news conference after the meeting, Barry suggested that suburban elected officials could be of considerable help in the stadium effort.

"Fairfax has outstanding business people," the mayor said.

"We're going to need that involvement."

Stressing that the Redskins are a "regional team," he noted that area localities have cooperated before on issues relating to "water, transportation and Metro, so we are accustomed to working together."

Barry said that one way a substantial amount of money for a new stadium could be generated is from the advance sale of luxury skyboxes, a major source of revenue for most National Football League teams that is not shared by the Redskins.

Barry and Herrity said they would convene a meeting of officials from various counties in October to discuss the ways that money could be raised for a new stadium.

"There's no question that this would have to be a public-private partnership," Herrity said.

The board chairman noted that plans for a new county government complex developed in partnership with a private developer were approved this year, "so there is some experience working together."

Asked whether he would be willing to commit taxpayers' money to aid the public part of that alliance, Herrity said: "I'm not saying that at all. I'm willing to commit private financing."