D.C. Mayor Marion Barry named Thomas M. Downs city administrator yesterday and announced several other high-level staff changes. The mayor also said he plans to more closely oversee the awarding of city contracts.

Barry said the changes are part of a continuing effort to bring the machinery of city government firmly under his control.

"I intend to hold the reins pretty tightly during my second administration," the mayor said.

As city administrator, Downs will also hold the title of deputy mayor for operations. Downs, current director of public works and the Department of Transportation, replaces Elijah B. Rogers, who is leaving May 27 to take a job with a private accounting firm.

John E. Touchstone, the head of the Department of General Services, will replace Downs as public works director, giving Touchstone--who has been in city government four months--expanded responsibilities over two other major city departments, Transportation and Environmental Services, in addition to retaining jurisdiction over General Services.

The new appointments are the latest moves in a major reorganization of the Barry administration that was launched at the beginning of his second term in January and led to the creation of three deputy mayor jobs.

In his post, Downs will have responsibility for overseeing most city agencies. But unlike Rogers, who had broad powers over the entire city bureaucracy, Downs will share duties with Ivanhoe Donaldson, deputy mayor for economic development and Barry's top political adviser, and Alphonse G. Hill, deputy mayor for financial management.

Barry's statement that he intends to increase his authority over city contracts comes while he has been embroiled in a dispute with the D.C. Lottery Board over the award of a key contract.

Under pressure from Barry, who called it a "runaway board," the board this week agreed to reopen bids.

Barry noted that he will soon have the opportunity to fill two seats on the lottery board and said he will not tamper with the quasi-independent agency's separate contracting authority.

But, Barry said, he wants more control over contracts handed out by other city agencies, particularly those in which department heads can sign contracts worth up to $5 million without the mayor's approval. "That's quite a bit of authority," Barry said. "I intend to narrow that."

Barry said that a plan to merge General Services, Transportation and Environmental Services into a single public works department will be submitted to the City Council for approval after Labor Day.

Touchstone, the new public works chief, was an official for 10 years with the Metropolitan Washington Council of Governments before joining the city government in Janu- ary.

Barry said that William B. Johnson, director of Environmental Services, will become a deputy director of public works.

An Office of Administrative Services also will be created, to handle housekeeping duties such as printing and telephone operations now done by General Services, and will be headed by Jose Gutierrez, the current city personnel chief.

Gutierrez will be replaced as personnel head by Clinton Hilliard, Montgomery County personnel director.

Avis Hawkins, deputy director of the Office of Documents, will step up to director, replacing David Splitt, who has left to practice law.

Downs now becomes the highest-ranking white official in the Barry administration. "There will probably be some in the community who will look at this as a question of race," Barry said.

"They shouldn't do that. Mr. Downs is competent and compassionate."

Downs, 40, a former city manager of Leavenworth, Kan., was brought into the city government by Rogers, the man he is replacing as city administrator.

He has represented the mayor on the Metro Board since becoming transportation director in January 1981. He had also previously worked in the U.S. Department of Transportation.