D.C. Mayor Marion Barry, saying he would do "everything in my power" to keep the Washington Redskins in the city, announced plans yesterday to retain a consulting firm to explore the possibility of building a 75,000-seat stadium for the football team.

The announcement came a day after a meeting between Barry and Redskins owner Jack Kent Cooke, who has expressed his desire for a 75,000-seat domed arena to replace Robert F. Kennedy Stadium. Cooke says RFK, which seats 55,000, is too small, and he has hinted that the team might move to the suburbs if his demands are not met.

Fairfax County officials met with Cooke for about 45 minutes yesterday at his estate in Middleburg, Va. Afterward, Fairfax County Executive J. Hamilton Lambert said the delegation mainly expressed concern that the Redskins remain in the Washington region, but he added, "We did not foreclose the option of a site in Fairfax County."

In his first public response to Cooke, Barry expressed a strong commitment to keeping the Redskins inside the city limits. "I'll do everything in my power to keep the Redskins in Washington," he said. "I am confident we will find a way."

Consultants are to explore several options aimed at satisfying Cooke and the Redskins, according to John White, the mayor's spokesman. One is building a new open-air stadium, which would cost between $110 million and $125 million, White said. No site has been identified.

Another option is renovating and expanding RFK Stadium, which could add about 10,000 seats, according to White.

Fairfax officials plan to meet with Barry to offer advice and technical support, according to Lambert.

"Cooke is enlisting our cooperation in working with Marion Barry," Lambert said.

"This isn't a game of bidding for the Redskins. It's a game of ensuring they remain in the metropolitan area."

In a telephone interview yesterday, Cooke repeated his preference for a new stadium in Washington. But he added, "If the stadium can't be built with the requisite parking and the amenities that usually attend these great enterprises, then of course we'll be very happy to consider one of the surrounding counties."

Some dismiss Cooke's threat as a bargaining ploy, noting that the Redskins' 30-year lease at RFK Stadium must be renegotiated when it expires after the 1990 season. But others say they are convinced that the 74-year-old communications and real estate magnate means business.

RFK is the third smallest stadium in the National Football League. The waiting list for season tickets has 20,000 names. In addition, RFK is one of the few stadiums in the league that does not have luxury skyboxes, a major source of income for NFL franchises.

Suburban officials responded to Cooke's tantalizing suggestion almost immediately. In addition to Fairfax, Prince William, Loudoun, Prince George's and Montgomery counties have expressed varying levels of interest in being host to the team.

The Barry administration is taking the situation seriously as well. The Redskins "are a major factor in the District's economic picture," said White. Moreover, he said, "They're part of Washington's heritage and tradition."

During a 90-minute meeting Monday in Middleburg, "Cooke and I agreed that we both want the team to stay in the District," Barry said.

Significant differences remain, however, primarily over Cooke's insistence on a domed stadium.

Cooke said yesterday that a domed stadium, while unnecessary for football, would help the city qualify as a site for the Super Bowl. In addition, he said, it would mean that the facility could be rented for concerts and other events without regard to weather.

"I much prefer a stadium without a dome," he said, "but I think the financial considerations" make it necessary. In the meeting with Fairfax officials yesterday, Cooke raised the possibility of a removable dome, according to Fairfax Board Chairman John F. Herrity.

Barry does not want a stadium with a dome because "he likes natural grass as a football fan," said White.

Despite the different views, Cooke said he was encouraged by the mayor's response during the meeting. "I was very pleased," he said. "It was a meeting of consequence. I might even say vigorous consequence."

According to participants in yesterday's meeting, Cooke assured the Fairfax delegation that he had no intention of leaving the region. "What Cooke and Jack {Herrity} discussed is whether we can help Marion Barry," Lambert said. "No one was out there trying to sell {Cooke} sites or come up with any financing mechanisms."

But officials did not rule out the possibility of a new stadium in Fairfax. "If it looks like the most feasible thing, we'd take a look at it like any other land-use plan," Herrity said.

Cooke has made it clear that he does not want to pay for a new stadium, a position that he defended yesterday by invoking an observation from columnist George Will: "The Redskins happen to be the most unifying force in the city of Washington."