Mayor Marion Barry yesterday asked the City Council to confirm two Hispanics, currently serving as acting department heads, as administrators of their agencies -- Jose Gutierrez as director of personnel, and Willie Vazquez as director of the Office of Latino Affairs.

The move is intended to please a constituency that supported Barry in 1978 and remains largely supportive, but which had recently received little attention from the administration, according to sources close to the mayor.

"I think he [Barry] wanted to announce both appointments on the same day," said a Barry aide. "They [Hispanics] are a constituency, and we think, a strong one."

Gutierrez, 34, has served as acting director of personnel since April 1979.

But, administration officials explained, he could not be elevated to director until last Dec. 27, when former personnel director George Harrod resigned.

Harrod, representative in many ways of a segment of black Washington with whom Barry has never done well, was transferred from his post as personnel director in February 1979 after being accused of sexual harassment. The charges are still pending in court, and he was considered something of an embarrassment to the administration, sources said.

Though he was working as an assistant to City Administrator Elijah B. Rogers, Harrod technically retained the post of personnel director until his retirement paved the way for Gutierrez to be promoted.

As acting director of personnel, Gutierrez oversaw the layoffs and job reductions ordered by Barry last year as part of the administration's effort to handle the city's budget crisis. He will be a key figure in the city's new bargaining relationship with public employe unions, and the overall development of the city's relatively new personnel system. His salary is and would remain $50,112.

Vazquez, 33, has served as acting director of the Office of Latino Affairs since former director Aida Berio resigned last October. His salary is and would remain $42,874.

Sources said Barry's choice was between Vazquez and Carlos Rosario, who was latino affairs director under former mayor Walter E. Washington, and that Barry chose Vazquez after deciding that he enjoyed more support in the city's Hispanic community.

"Rosario represented people who have been around a long time, people who maybe are a little bit afraid -- the do-nothings," said one Hispanic activist. "I think Willie had more support among young people."

The competition between Rosario and Vazquez reached a head two weeks ago when Rosario led a group of about 40 persons, most of them senior citizens, to demonstrate on his behalf at the District Building. Barry interviewed both men last Thursday, sources said, and decided that "Vazquez was clearly the better candidate."

Community leaders who backed Vazquez for the job said that in the past the office has spent most of its efforts complaining, while they believe Vazquez is more knowledgeable about various government and private sector aid programs and how to apply them.