MCI Communications Corp., a rapidly growing local telecommunications firm which is competing with the Bell System for large-volume intercity communications business, has signed Washington's largest non-governmental office lease.

The company, whose offices are scattered in downtown Washington, plans to lease 183,000 square feet of space in a new building under construction at 1137 19th St. NW, according to a company official.

The building also has a first-floor commercial space available which is believed to be under consideration by restaurateur Duke Zeibert as a possible site for his new restaurant.

The building is expected to be completed by Jan. 1, 1981, said Wayne English, MCI's chief financial officer. Leasing arrangements for the proposed 12-story structure, all of which will be leased for MCI headquarters except the first floor commercial space, were handled by the H.G. Smithy Co.

The new building will be around the corner from the Federal Communications Commission offices.

The Supreme Court last year refused to block a decision of the U.S. Court of Appeals for the District of Columbia requiring American Telephone and Telegraph Co. to make more local exchange facilities immediately available to MCI for its Execu-net long-distance phone service. The company has been expanding ever since.