Washington school Superintended Vincent E. Reed, responding to a drop in enrollment and completion of a major building program, yesterday proposed closing 13 of the city's 126 elementary schools and three of 31 junior highs.

In a report to the city school board, Reed also suggested moving school administration headquarters out of a downtown office building to Lincoln Junior High at 16th and Irving Streets NW.

Lincoln was opened in 1967, and since has been troubled by serious problems of discipline and vandalism. Under Reed's proposal, Lincoln would be phased out as a school in June 1980.

In addition, the superintendent proposed closing two buildings used for special senior high school programs, two centers for handicapped students and six other old schools now used as classroom annexes and offices. All the proposals must be considered at public hearings and acted on by the D.C. school board.

"This would be one of the biggest changes that's ever happened to this school system," Reed said. "It's a tough decision, not a popular one for sure. I understand the anxieties people have about losing schools. But we have to close some schools to maximize benefits for our students."

Reed estimated the proposed closings would save $600,000 next year and much more after that as the number of school administrators is reduced by retirements. The superintendent noted that under board rules all tenured administrators whose buildings are closed are guaranteed jobs elsewhere in the school system.

Because of new cosntruction and the cluster of schools in some neighborhoods, Reed promised that virtually all children who now walk to school will continue to do so.

The proposed school closings in Washington are part of a nationwide pattern caused by a downturn in births. School systems in the Maryland and Virginia suburbs are involved in this trend.

However, until now the D.C. school system has made no major move to close unneeded classrooms.

Last fall the General Accounting Office reported the school system had 19,000 excess seats in elementary schools and would have a surplus of 28,000 by 1980.

Total enrollment has dropped from a peak of 149,116 in 1969 to just under 120,000 this year - a decline of 19.5 percent.

But during the past decade the city has carried out the largest school building program in history, spending more than $300 million for more than 40 new schools and major additions.

Two of the junior highs recommended for closing - Lincoln and Hamliton at 6th Street and Brentwood Parkway, NE - were opened just 10 years ago. Both have been plagued by discipline and vandalism problems.

Reed said conditions at both of these schools improved this year, but that enrollment at both is now more than one-third below capacity.

The third junior high earmarked for closing is Gordon at 35th and T streets NW, in Georgetown. Reed said the school has no seventh graders this year because many of its feeder elementary schools have added junior high programs.

The superintendent said he rejected a proposal, first made by a parents' group two years ago, to turn Gordon into a rigorous academic high school students turning in the area is too low.

Instead, he said the building would probably be used for several years for programs of the Ellington High School for the Arts. Ellington occupies old Western High School, about two blocks away, which is scheduled to undergo major renovation.

Reed said 14 of the buildings recommended for closing would be turned over to the D.C. Department of General Services to be sold or torn down. Three old buildings - Slater and Langston at North Capitol and P streets, and Giddings, at 3rd and G streets SE, would be demolished to provide more space for playgrounds of nearby schools.

The other nine buildings involved, Reed said, would be used for other school programs. Among them, he said, are the two special senior high programs, the Randall Aerospace and Marine Science school in Southwest and the School Without Walls, at 1619 M St. NW, whose present buildings Reed wants to vacate.