The District of Columbia is applying for a $1.6 million federal grant to help turn 12 blocks of F Street NW in downtown Washington into a pedestrian mall.

It also is asking for a $2 million federal grant to buy 20 small, fuel-efficient buses, which Metro would operate on routes that have low ridership.

The chances of the city getting the grants are "iffy," however, according to city Transportation Director Thomas M. Downs. Both grants are under fiscal 1981 federal programs, for which funds already have been appropriated by Congress, but "it's unclear whether the grant funds will be impounded" by the Reagan administration, Downs said last week.

The grant for the F Street mall would be used for a feasibility study to determine how much of the area between Third and 15th streets NW could be incorporated into the project. This would involve a decision about whether to include the existing mall between 12th and 14th streets NW, which is now open to traffic.

The proposed mall would be open only to pedestrians, Metrobuses and "Downtowners," the smaller, lower-cost buses that serve the F Street business district and Southwest Washington.

The grant -- which would come from a U.S. Transportation Department program for innovative urban projects -- also would enable the city to design the mall and begin construction. The remainder of the funding would come from other sources, and city officials say both the Pennsylvania Avenue Development Corp. and the Metropolitan Washington Board of Trade have expressed interest in the project.

Turning F Street NW into a pedestrian mall has been proposed as a way of improving business in downtown Washington ever since the early 1960s, when stores began losing customers to suburban shopping centers.

In 1966, the mall between 12th and 14th streets NW was built. It has faced several difficulties, including the fact that auto pollution, poor drainage and poor soil have either killed or stunted its trees, leaving it a barren island in the middle of the street.

In 1974, the $6 million Streets for People projects created two other malls, closing a two-block section of F Street NW opposite the National Museum of American Art (formerly the National Collection of Fine Arts) and a one-block section of G Street NW beside the Martin Luther King Jr. Memorial Library.

Despite these efforts, downtown businesses have continued to lose revenue. But District officials still feel that an extensive, well-designed mall -- particularly on F Street NW, historically the city's premier shopping street -- could entice customers back downtown.

Additional support for the idea came recently from the Board of Trade, which urged the city in a study of downtown released last month to "minimize" motor vehicle traffic on F Street NW and cut down parking on G Street NW to further reduce traffic.

The other federal grant the city is seeking would be used to buy buses similar to the Downtowners or those used in Montgomery County's popular Ride-On program. District officials say the fuel-efficient buses would benefit the Washington area by helping to lower Metrobus costs, which are paid by the District and neighboring jurisdictions.

Metro would determine on which routes the small buses would be used. The funding would come from the new bus equipment program of the Urban Mass Transit Administration.