Mayor Walter E. Washington's city administration, stung by reports that a key minority-contracting program is lagging, released a report yesterday showing a sharp increase in the flow of city dollars to minority firms.

James W. Baldwin, director of the D.C. Office of Human Rights, said 18.5 percent of the money for contracts of more than $10,000 went to minority firms in the first five months of the 1978 fiscal year, which began last Oct. 1.

This compares with 12.8 percent in the full 1977 fiscal year, and 8.8 percent in 1976, Baldwin said.

Baldwin stressed that his report to the mayor was routine. But its handling by the mayor's press office was far from routine. Where such reports are rarely issued to reporters, the press office prepared a release on its findings.

What made the difference was a recent news report dealing with the D.C. Minority Business Opportunity Commission.The news report said the commission spent almost an entire year and failed to channel up to $85 million in contracts earmarked for minority entrepreneurs.

Joseph P. Yeldell, general assistant to the mayor, acknowledged that "we have not gotien (that) program where it ought to be, but it has not impacted on (other) minority contracting. Jim Baldwin's report shows it is on the up-swing."

Under a mayorol order issued in 1973, the office of Human Rights reviews all contracts made by city agencies for more than $10,000 for evidence of actions designed to increase minority participation.

Between last Oct. 1, the start of the 1978 fiscal year, and Feb. 28 the city's four construction agencies awarded 89 contracts totaling $47 million, Baldwin found. Of those, 24 1/2 contracts totaling $8.7 million or 18.5 percent of the total, went to minority firms.

Of the minority contracts, 4 1/2 totaling $789,314 were awarded by the Department of General Services; 10 totaling $3.9 million were awarded by the Department of Transportation, and 10 totaling $4 million were awarded by the Department of Housing and Community Development.

None of the three contracts totaling $22.8 million that were awarded by the Department of Envoronmental Services went to minority firms.

Baldwin said the record is especially good, since the city's public works program this year has been curtail because Congress has not enacted a formal budget for the city. The city is operating under a stopgap resolution that keeps most routine spending at last year's levels and does not authorize any new construction projects.

So-called "local public works" contracts, financed by the U.S. government rather than from the city budget, made up 28.4 percent of the construction contracts that have been awarded by the city this year, Baldwin said.

Federal law requires that at least 10 percent of the contracts under that program go to minorities. The city actually awarded 40.7 percent of those contracts to minority firms.