Two of the chief contenders in the Sept. 12 Democratic mayoral primary, Mayor Walter E. Washington and City Council Chairman Sterling Tucker, used this weekend's Hispanic American Festival as the occasion for an exchange of charges about who is doing more for the estimated 60,000 Spanish-speaking people in th city.

Tucker, who has issued a series of position papers and statements to systematically pinpoint what he sees as the shortcomings of Washington's administration, said the District government "has a deaf ear turned to Hispanic problems" in the city.

The mayor, in a statement delivered at the festival, responded that "it is the height of irresponsibility - or of ignorance - to say that the city government has turned a 'deaf ear' to the needs of the city's Latino residents. Our ears are not deaf to their needs. We hear them clearly; we are acting on what we hear."

Tucker, in a statement his aides handed out in Spanish and English at the festival, said the city government "hasn't the foggiest notion about what to do about Hispanic exploitation, unemployment and underemployment." He charged that the administration lacks a housing plan for Latinos and has no program to reach Hispanics to inform them of available city services.

"In sum," Tucker said, "the current administration treats the Hispanic community as non-existent - not seeing them, not hearing them and certainly not serving them."

Meanwhile, in his statement, Washington touched on a recurring theme in his campaign speeches - his contention that while problems remain in the city government, his record in the last 3 1/2 years is one of accomplishment.

"We have come a long way in assuring these programs to all our people without discrimination," the mayor said. "We still have away to go, but increasingly, we are putting programs in place to assure all Hispanic-Americans the opportunity for full participation in the life of this city."

He said about 250 Spanish-Americans are in the city government and decribed the figure as unsatisfactory. 'It is my goal," the mayor said, "to report to next year's festival a significant increase in the number of persons with Spanish background on the staff of the District agencies."

Washington said that one place where there is "room for improvement" in hiring hispanics is on the staff of the City Council, which Tucker heads. The mayor said that as of Jan. 1, 1977, there were "precisely zero" hispanic-Americans employed by the City Council.

According to one two-year-old estimate, 5,000 to 7,000 Hispanics registered to vote in the District. Although that is a relatively small percentage of the estimated 183,000 registered Democrats eligible to vote in the party primary, the election is expected to be close and each segment of the District's population could be a deciding factor if it were to line up solidly behind one candidate.

With that in mind, Tucker, Washington and the third major contender City Councilman Marion Barry, all visited the festival yesterday.

Barry workers handed out a green flyer, with English on one side and Spanish on the other, listing eight reasons why he should be elected mayor. Barry's flyer, among other things, said the he co-sponsored the bill creating the city's Office of Latino Affairs and supports bilingual education "as a means of developing knowledge and understanding of the different cultures represented in our city."

Tucker, in his position paper, said that if he is elected mayor his administration "will want and will need the participation of Latinos in the municipal government as the first step toward bringing the Hispanic community into the mainstream of the District's life."

The City Council chairman said he would "demand that every District agency make a serious effort to recruit, train and promote Latinos in all job classifications, including planning and policy-making positions."