The U.S. Department of Transportation yesterday formally relaxed its previous opposition to a special direct federal appropriation for completing the Washington Metro system, but restated its conditions for continued federal involvement in Metro construction.

In testimony before the regional affairs subcommittee of the House District of Columbia Committee yesterday, Assistant Secretary Mortimer L. Downey III said the department "has reached no final conclusion" on special appropriations to complete Metro.

Transportation Secretary Brock Adams had said last year that he opposed such a special bill because he doubted it could win support in Congress.

Downey's revision of that position came in hearings on special Metro appropriations. There have been unofficial indications that DOT would actually support such legislation if Metro could find guaranteed local finances for operating and construction costs.

Additional federal money would be needed about 1982 when, it is projected, Metro will have exhausted money transferred from once-planned interstate highway programs in the Washington area. The total additional amount needed is estimated at about $1.7 billion, bringing total cost of the 101-mile Metro system to $7 billion.

Metro's program is so large that there has been some pressure from other cities to keep Metro out of the general pot for major transit improvements.

Before the federal government can move ahead with the Metro program, Downey said, it must know how and when local governments will be able to make "full faith and credit" pledges to pay one-third of the cost of interest and principal on $1 billion in federally guaranteed bonds sold to build Metro.

A tentative agreement was negotiated in December under which the federal government would pay two-thirds of the bonds and the local governments one-third, but the details have never been worked out.

In a letter last week to Metro Board Chairman Jerry A. Moore Jr., Deputy Transportation Secretary Alan Butchman wrote the Metro construction program for the current fiscal year - 1979 - also would be held up until the "full faith and credit" problem is resolved.Included in that program is an authorization to purchase about 90 badly needed new subway cars, according to sources.

Downey, in his testimony yesterday, opposed special federal assistance for operationg costs to the Washington Metro, saying that Washington should receive no more operating aid than other cities of similar size. Washington presently participates in a nation-wide federal subsidy program.

D.C. Mayor Marion Barry, in testimony, told the subcommittee yesterday that the District's commitment to the 101-mile system is unwavering. He suggested that an appropriate dedicated tax for Metro expenses might be a regionwide payroll tax.