James T. Eynn, former director of the Office of Management and Budget, was chosen yesterday as president of the Federal City Council, an influential nonprofit group that studies key problems in the Washington area.

Lynnl 51, a lawyer, succeeded Sol M. Linowitz, who had been the council's president since 1974. Linowitz, a lawyer specializing in international affairs, is a former Xerox Corp. chairman and former U.S. ambassador to the Organization of American states. Linowitz also was a U.S. negotiator of the recent Panama Canal treaties.

Lynn, a partner in Jones, Day, Reavis & Pogue, took over as Federal City Council president yesterday, beginning a one-year term. Council presidents normally serve several terms. In addition to heading OMB during the Ford administration, Lynn also has served as secretary of housing and urban development and undersecretary of commerce.@n a speech to about 125 council members and in an interview afterward, Lynn said he had not decided what issues he would seek to make the focus of council activities. He said he planned to talk with city and congressional officials and the council's own staff before "formulating an agenda" for the council.

In a luncheon speech at the Madison Hotel. Linowitz urged the council to consider organizing a task force of business and other nongovernment groups to draw up plans for future development of the Washington area. He said such a task force should examine issues ranging from teen-age unemployment to the problems of low-in-come city residents who have been displaced by high-priced residential and commercial development projects.

The Federal City Council organized in 1954, includes representatives of 100 business, professional and non-profit organizations. It was formed by a group of business executives, including Phillip Graham the late publisher of The Washington Post, as a counterpart to the Metropolitan Washington Board of Trade, which the council's founders viewed at the time as too conservative.

In recent years, its recommendations have included completion of the proposed 100-mile Metro subway system and establishment of a regional tax to pay for it. It also has supported city plans for construction of a downtown convention center. Another council-sponsored study recommended increased participation in public affairs by local businesses as well as an expanded White House liaison office to deal with regional affairs in the Washington area.