The General Services Administration announced yesterday that it has asked Congress for authority to start work on two giant government office, retail and exhibition buildings to complete the Federal Triangle, replacing a huge parking lot behind the District Building.

As the first step toward bringing the project to reality, GSA officials said they will ask the Commission of Fine Arts and the National Capital Planning Commission to endorse the plans at meetings during the next two months.

David Dibner, GSA's assistant commissioner of public buildings for design and construction, estimated at a news conference that the project could cost $350 million and take five or six years to complete. He said it would house federal agencies that now are located in privately owned, leased buildings.

The proposal represents the scrapping of a 1930 plan to convert the parking lot into the Great Plaza, a formally landscaped open space with a parking garage beneath.

Both interconnected 10-story buildings would be erected on the L-shaped parking lot, one fronting on Pennsylvania Avenue between 13th Street NW and the five-story District Building, and the other fronting on 14th Street NW and facing the mammoth Commerce Department headquarters. A two-level underground parking garage would provide space for about 2,000 cars.

The proposal also would introduce a more contemporary form of architecture alongside the Triangle's neoclassic Greek-temple style. "We are looking for something that reflects today and respects yesterday," Dibner declared.

Under the GSA master plan, prepared by the architectural firm of Harry Weese and Associates, the 14th Street building would have two separate wings wrapped around a high, glassed-in galleria.

The galleria would form part of a sheltered promenade between the Commerce Department building, the nearby Federal Triangle subway station and the restored Old Post Office Building at 12th and Pennsylvania. It also would provide exhibit areas for historic collections from the National Archives.

The bottom three floors of both proposed new buildings would be available for other exhibits, shops, restaurants and the like, although they also could be used, like the upper stories, for offices.

GSA officials said that they recently filed a prospectus, a formal request to authorize spending $3.5 million on construction plans, with the two congressional public works committees. If granted, this would be followed next year by a prospectus seeking authority for construction. Dibner said the project architect will be chosen by a brief, limited national competition once the planning money is available.

By law, approval by the congressional committees is the only step needed to authorize the project. Funds needed to do the work, however, must be included by the administration in the federal budget. The$3.5 million in planning money is in President Reagan's pending budget for the GSA.

Plans for the massive construction project had drawn little attention outside the federal bureaucracy until last October, when The Washington Post obtained the draft of a proposed environmental impact statement. Yesterday GSA unveiled the Weese firm's 110-page master plan containing details, schematics and proposed architectural outlines.

It would scale down the originally projected occupancy of the two new buildings from 9,000 to about 5,000. The rest of the Federal Triangle, which stretches from Sixth to 15th streets between Constitution and Pennsylvania avenues, already houses about 20,000 government workers.

In addition to the new buildings, the plan calls for slightly enlarging and finishing, in its original classic style, a raw brick end to a wing of the Internal Revenue Service building at 11th and Pennsylvania. A similar raw brick wall on the west side of the building that houses the Ben Franklin Post Office branch at 13th and Pennsylvania also would be finished.

Another part of the project would be the so-called Federal Walk, linking points of artistic and historic interest, including the now inacessible courtyards in Triangle buildings. Robert J. (Jerry) Karn, vice president of the Weese firm, said this would eliminate the Triangle's "Chinese wall" effect of serving as a barrier between downtown Washington and the Mall.