Katharine Graham, chairman of the Washington Post Company, yesterday called on the Federal City Council, an organization of influential business and professional interests in Washington, to expand its membership to represent more broadly the community it serves.

"I think we should face up to the charge that we are an exclusive group," said Graham. "The issue is whether we are exercising whatever power we possess responsibly and fairly and in the interests of our community."

Graham said the council should continue to be a valuable behind-the-scenes force in the city. But the council must also expand its membership for "broader community representation," she said.

Former Washington Post publisher Philip L. Graham was one of the founders of the council, which has helped shape policy in the area through its support of such projects as the subway system and the convention center.

Graham noted that the council faces a different set of problems now than it did in 1954, when urban blight and suburban expansion were major issues. Although the suburbs have continued to grow, the city is enjoying a revival, she said.

Former Secretary of Housing and Urban Development James L. Lynn was reelected president of the Federal City Council. Vincent C. Burke Jr., chairman of Riggs National Bank, was elected chairman of the group, replacing Donald S. Bittinger, retired chairman of the Washington Gas Light Co. Phillips S. Peter vice president of General Electric Co. was elected vic president, replacing Thorton W. Owen, chairman emeritus of Perpetual Federal Savings & Loan Association.