Some of Washington's most influential business leaders, bolstered by a new study from the respected Stanford Research Institute International, have begun a major effort to redefine the role of the private sector in metropolitan affairs here.

The study sponsored by the Federal City Council, recommends among other things that business interests take a more public role in area affairs and that the White House convert its District of Columbia liaison office to one with regionwide interests.

The study already is being read at the White House and was presented to 30 influential business leaders Monday night. It was written by Thomas Fletcher, a deputy mayor of the District of Columbia before home rule, and a man highly respected here for his understanding of the region's politics and business.

A central conclusion is that the private sector's activities are badly fragmented, with various groups bumping into each other as they attempt to deal with problems ranging from support for the arts to studies of demographic trends in Prince George's County.

Fletcher, in a telephone interview, explained that he saw a White House office with regionwide interests playing a role similar to that a major industrial employer would pay in other cities.

"Look at any other of the major cities," Fletcher said, "and one or two or three industries provide the clout. That's missing in the District of Columbia because the major employer is the federal government."

The White House regional office, he said in his report, should be a "powerful neutral to provide the process for problem resolution - not to direct but to facilitate."

That was only one of six recommendations contained in the $12,000 study. Fletcher interviewed 65 business, government and civic leaders last summer in preparing the study, then met with a number of them in November to sharpen his findings.

The study itself was commissioned as a result of "uneasiness in the private sector that we didn't have our act together," according to Sol M. Linowitz, president of the Federal City Council. The council is made up of the most influential business and professional leaders in the area.

Linowitz and his brother, R. Robert Linowes, president of the Metropolitan Washington Board of Trade, also said yesterday that the private sector has to take a more public, up-front position on local issues if it expects to have impact.

That agrees with a central statement of Fletcher's report:

"Businessmen would rather stay in the background and be influential in private. But they are probably going to lose the important battles if they continue to use these tactics. This is particularly true with the system of participation and confrontation that has become a way of life in urban government today."

If the private sector is to speak effectively, the report suggests, it needs to redefine the roles of its key players to reduce inefficiency and overlapping.

Among other things, the report recommends:

That the Washington Center for Metropolitan Studies be merged with the Municipal Research Bureau. The Center does regionwide studies on such topics as growth and transportation. The Bureau has concentrated on District of Columbia financial affairs. The merger would result in a research group with regionwide interest in growth and government finances.

That the Federal City Council concentrate on following government planning, policy and program implementation. The council would provide a strong link between area interests and the White House and Capitol Hill.

That the board of trade be primarily responsible for business promotion, economic development and related activities.

Linowes stressed that the board of trade was not planning a power play to absorb the other 20 or so chambers of commerce in the area. Rather, he said, "we would try to coordinate" efforts of the various groups so they would be more effective.

The report also said the business community should decide whether and how to support fully the Community Foundation for Greater Washington, a little known organization that could be turned into a regional mechanism for handling the business community's philanthropy.

The recommendation for a White House office with regional instead of local interests is certain to stir debate. Under the Carter administration, the White House District liaison office has been less active than in some previous years. D.C. government officials fondly remember the years when Egil (Bud) Krogh, for example, handled District affairs in the Nixon administration.

Krogh later was sucked up in the Watergate scandal, but was regarded as an effective advocate and accessible contact point for District of Columbia problems.

Representatives of the Federal City Council already have met with staff members for Vice President Mondale's office to discuss the report with them. The Mondale staff is preparing to support legislation for greater District of Columbia autonomy.

Paul Reichardt, chairman of Washington Gas Light and also of the board for the Washington Center for Metropolitan Studies, called the recommended merger of the center with the Municipal Research Bureau "strictly a concept." However, he said, "it has merit. But there are no detailed studies on what this animal will look alike."

The merger was recommended, Fletcher said, because of a complaint he heard frequently during his interviews to the effect that no one was collecting the data the business community needs in a logical, regionwide way.

"There's no shortage of data, of leadership or of money in the Washington area," Fletcher said.

His proposals now will be discussed by the various boards representating community business interests.