Influential members of Congress, in the most serious challenge to the District of Columbia's five-year-old home rule law-making powers, have introduced legislation to overturn a City Council bill designed to keep foreign embassy offices out of residential neighborhoods.

A resolution to veto the council bill was introduced yesterday by Sen. Frank Church (D-Idaho), chairman of the Foreign Relations Committee, and cosponsored by three committee members. A similar resolution was introduced in the House by Rep. Clement J. Zablocki (D-Wis.), chairman of the House Foreign Affairs Committee, and cosponsored by six others.

They have responded to lobbying efforts by the State Department, which declared in a statement circulated on Capitol Hill that the council bill represented excessive "interference with the conduct of foreign relations."

Both chambers of Congress, moving swiftly on the veto measures, have scheduled hearings for next week -- the D.C. subcommittee of the Senate Governmental Affairs Committee on Monday, a House District subcommittee on Wednesday.

If approved, the resolution would be the first congressional veto of a D.C. City Council bill since limited home rule began in 1975.

The Home Rule Charter allows Congress to override council-passed bills within 30 legislative days after they are received for review after being signed by the mayor. Since 1975, six resolutions to overturn bills have been introduced, but none has passed. Only one, dealing with the city's financial operations, came close to approval in 1976.

The council passed the challenged bill on Oct. 9 and Barry signed it on Nov. 9. It would prevent embassies from locating future offices, called chanceries, in residential neighborhoods -- chiefly in the Embassy Row areas along Massachusetts Avenue NW west of Dupont Circle and 16th Street north of Scott Circle.

Residents of those areas have long argued that additional chanceries would overcrowd their tree-lined streets with traffic and cause other disruptions.

The chief sponsors of the council bill, Polly Shackleton (D-Ward 3) and David A. Clarke (D-Ward 1), argued that the chanceries belong in office buildings outside residential neighborhoods.

But the State Department in its document, contended that the restrictions in Washington would make it difficult for the United States to obtain suitable sites and concessions for operating its embassies in other countries.

The District government, the State Department, asserted in its lobbying document, has become "increasingly unresponsive to the needs of the federal government."

Leading the push for passage of the veto resolution in the House is Rep. Fortney H. (Pete) Stark (D-Calif.), an author of the city's Home Rule Charter, who said he regretted having to assume the role.

In passing the chancery bill, Stark said the Council exceeded its authority by overturning less restrictive chancery regulations adopted by the National Capital Planning Commission and the D.C. Zoning Commission.

Joining Church in sponsoring the Senate resolution were Sens. Claiborne Pell (D-R.I.), Jacob K. Javits (R-N.Y.), and Charles H. Percy (R-Ill.). Joining Zablocki and Stark in sponsoring the House Bill were Reps. Dante B. Fascell (D-Fla.), William Broomfield (R-Mich.) and Millicent Fenwick (R-N.J.), members of the Foreign Affairs Committee; Reps. Jack Brooks (D-Texas), chairman of the Government Operations Committee, and Charles Wilson (D-Texas), chairman of the House D.C. Appropriations Subcommittee. Fenwick is also on the D.C. committee.

Under the Home Rule Charter, a legislative day in Congress is defined as a day in which either chamber is in session. Yesterday was the 16th of the 30 legislative days in which Congress may act to veto the chancery bill. The time will run out sometime in January, after Congress reassembles following the congressional holiday recess.

In a related development, the D.C. Federation of Citizens Associations has adopted a resolution strongly opposing a congressional veto of the bill.