The General Services Administration has convinced 13 building owners who rent significant blocks of office space in the District to the federal government to challenge city tax assessments as part of a pilot project.

GSA Public Building Commissioner Richard O. Haase said the challenges may prove to be a viable way to keep down escalating costs that are built into government leases, costs that landlords are allowed to pass on directly to the federal government.

Overall, the 13 buildings have an assessed value of $203.8 million for tax year 1984, which begins in July.

Ernest C. Vernon, a GSA public utilities specialist who negotiated with the landlords, said "we don't know how much we could save, but it could be substantial."

The District's tax rate is $2.13 per $100 of assessed value. Federal agency tenants occupy between 79 and 100 percent of the various buildings. The percentage of occupancy has a direct correlation with the percentage of the city property tax that the federal taxpayer must bear.

Vernon said GSA decided to let the building owners challenge the assessments before the District's Board of Equalization rather than have government intervenors do it because "it was easier. We're working closely with them."

The federally occupied buildings and the assessments that will be challenged are:

* Columbia Plaza, 2401 E St. NW, owned by Westwood Management, and fully occupied by federal agencies, primarily the Equal Employment Opportunity Commision and the Interior Department. $25 million.

* Franklin Square North, 1325 K St. NW, owned by Weaver Brothers, and 84 percent occupied by federal agencies, primarily the Federal Elections Commission. $7.5 million.

* Union Center Plaza North, 941 North Capitol St. NE, owned by Total Management, and 79 percent occupied by federal agencies, primarily the Energy Department and the Veterans Administration. $14.27 million.

* Union Center Plaza South, 825 North Capitol St. NE, owned by Total Management, and 80 percent occupied by the Federal Energy Regulatory Commission. $14.63 million.

* Imperial Building, 1441 L St. NW, owned by Shannon & Luchs, and 90 percent occupied by the Small Business Administration. $14.2 million.

* Chester A. Arthur Building, 425 I St. NW, owned by Dutch Property Management, with 98 percent federal occupancy, primarily by the Justice Department. $15.2 million.

* The Bicentennial Building, 601 E St. NW, owned by Sixth and E Associates and fully occupied by various federal agencies, including the Labor Department and the Department of Housing and Urban Development. $16.9 million.

* Federal Communications Commission headquarters, 1919 M St. NW, owned by Charles E. Smith, with 85 percent federal occupancy. $17.5 million.

* Donohoe Building, 400 6th St. SW, owned by Donohoe & Sons, and 88 percent federally occupied. $5.2 million.

* Indiana Building, 633 Indiana Ave. NW, owned by Indiana Associates, with 96 percent federal occupancy, primarily by the Federal Trade Commission and the Justice Department. $4.36 million.

* Patrick Henry Building at 601 D St. NW., owned by Virginia Corp., and 92 percent occupied by the Labor Department. $19.5 million.

* Buzzard's Point Building, 1900 Half St. SW, owned by Westwood Management, and 98 percent occupied by the Defense Department. $19.525 million.

* Transpoint Building at 2100 2nd St. SW, owned by Westwood Management, and 95 percent occupied by the U.S. Coast Guard. $20 million.

Haase said that getting the income-flow information from building managers was "difficult" in some cases, so new federal regulations may be drafted requiring building owners signing federal leases to provide that information to the GSA annually.