Continuing federal investigations into D.C. government corruption have cost Mayor Marion Barry political support throughout the District and increased skepticism about his personal integrity, according to a new Washington Post poll.

The poll of 513 city residents, conducted by telephone Aug. 10 to Aug. 21, found that two out of three respondents believe corruption is a major problem in D.C. government. More than half said that federal officials are justified in their investigations into alleged corruption in the Barry administration.

When asked to rate Barry's personal honesty and ethical standards, 47 percent of the respondents described them as "not good" or "poor" -- a nine-point increase from 13 months ago. Fewer than half of those interviewed, 44 percent, said they approve of the way Barry is handling his job, down six points from a July 1986 Post survey.

Nearly two-thirds of the respondents said that District contracting officials, who were the initial focus of the U.S. probe, are doing a "not good" or "poor" job. Half of them characterized District government as inefficient, and 53 percent said the mayor should not seek a fourth term in 1990.

Barry retained a strong core of support, however, among about one-fourth of all respondents, who consistently backed him and his administration. A slightly larger portion was equally intense in its opposition to him.

The poll also found continuing divisions in opinion between blacks and whites in the District, where 70 percent of the population is black and where Barry and his supporters have often characterized the mayor as a victim of racially motivated criticism and investigations. Barry was elected to a third term last year with overwhelming support from black voters and scant backing from whites.

On many of the key questions in the survey, about three of four whites polled offered negative opinions of Barry, his administration and the issues surrounding the corruption probe, while blacks were about evenly split on the same queries.

A majority of both blacks and whites said they thought U.S. Attorney Joseph E. diGenova's investigation of the Barry administration was motivated primarily by evidence of wrongdoing.

However, a large majority of blacks and a significant number of whites saw race, and to a much lesser degree, political considerations as secondary motivating factors. DiGenova is white and a Republican appointee; Barry is black and a Democrat.

Barry's approval rating among blacks dropped six points -- to 51 percent -- from last year's 57 percent approval rating. Among whites, it fell from 32 percent to 19.

Barry said he was "elated" with the 44 percent approval rating. "I am excited and encouraged that in one year {the approval rating has} dropped off about six {points} when we have had nothing but a daily dose of negative information about the Barry administration" in the news media, the mayor said in a telephone interview Friday from Chicago.

"That means that I have a solid base of support out there that believes in me and in this administration. It {the approval rating} should have been worse -- 20 or 25 percent -- given the daily dose of negative publicity."

In December 1984, a Washington Post poll found that 65 percent of the respondents felt Barry was doing a "good" or "excellent" job.

Political observers cautioned against premature dismissals of Barry's political future based on the poll results. They also said, however, that the most immediate impact could come in his ability to mobilize support for his policies and programs.

"His base probably still is fairly strong," said Edward J. Rollins, who as White House political director saw the recession drive President Reagan's approval ratings and influence to their lowest points. Both rebounded with the economic recovery; Reagan's approval rating now stands at 50 percent.

"It comes down to, can you govern efficiently and get public approval for your initiatives when that negative perception starts to build?" Rollins said.

The margin of sampling error for the overall results is plus or minus 5 percent. Among the poll's findings:Two out of three respondents said corruption is a "big problem" in District government. Almost two-thirds of blacks shared this view with three out of four white respondents.

Fifty-four percent of those surveyed said the continuing federal investigation of District government is justified. Another 32 percent said the probe was not justified, and the rest expressed no opinion.

More than half -- 56 percent -- said that Barry is doing a "not good" or "poor" job in making sure top government officials are honest.

Among blacks, a gender gap has emerged. While 59 percent of black men approved of the way Barry is handling his job, only 45 percent of black women polled agreed, a 14-point difference in opinion. There were smaller differences among whites.

The majority of those questioned said that race relations are staying about the same in the District, but only 23 percent say relations are improving, a drop of 14 percentage points in those who felt that way last year. Fifteen percent said race relations are worsening, as opposed to 8 percent who said they felt that way in the July 1986 poll.

Barry advisers and other political observers said that the overall results show the effect of what one described as a "media bombardment" surrounding the federal investigation of the District government.

Barry's standing has also been eroded, they said, because of a chain of events that includes poor snow removal last winter, disclosure of Barry's visits this year to the home of a 23-year-old model, and the guilty plea this year of former deputy mayor Alphonse G. Hill on fraud and tax evasion charges. That brought to 11 the number of top Barry aides who have pleaded guilty or been convicted of wrongdoing, including two deputy mayors.

There also have been continued disclosures from the federal investigations of close associates of the mayor, and renewed questions about the nature of his self-described "personal" relationship with convicted cocaine dealer Karen K. Johnson.

But the poll found divided opinions on whether Barry himself is directly involved in any wrongdoing, with 37 percent saying they believe he has broken the law, 36 percent saying just the opposite and 27 percent undecided.

"This thing will have to run its course," said Alvin Thornton, a Howard University political scientist, an observer of District politics and a Democratic political activist in neighboring Prince George's County. "The mayor will just have to hope that there is no indictment. If there is not an indictment that involves the mayor and he gets greater positive publicity about the things he is doing, I think he will weather the storm."

One leading black Democrat who lives in the District said that many blacks feel instinctively that race is a significant motivating factor behind the investigation.

"I think that it's a fair reflection of the sentiment of the black community that . . . whatever the wrongdoing that there is, is not unusual in municipal government," said the activist. "At the same time, I think there is increasing anxiety about the direction of government."

Peter Cojanis, 50, a white resident of the Petworth neighborhood in upper Northwest Washington, was one of those interviewed in the survey who said he thought Barry was doing an "excellent" job running the city. But he graded the ethical standards of Barry's aides as "poor," saying, "I don't think Mayor Barry is perfect.

"I believe there is a conspiracy against {Barry}," Cojanis said. "They don't have any evidence on the man that I can see or understand."

Deborah Robinson, 31, who lives in the Buena Vista neighborhood in Southeast, was one of the growing number of black women who disagreed. "There's something going on," said Robinson, a lifelong D.C. resident, who said race is not the reason the mayor is being investigated. "We've got to start somewhere. Why not get rid of him?"

Public confidence in Barry's performance is shaky enough that a majority of those surveyed said he should not seek reelection in 1990. But political observers, Barry advisers and the mayor himself said this finding is an indication of only a chink in his political armor.

Barry has tried in recent weeks to distance himself from the federal investigation by discrediting diGenova's efforts as "Mickey Mouse." The poll's finding that a majority of blacks and many whites see race and politics as secondary factors in the probe suggests the potential for a significant change in the way the probe is viewed if investigators misstep.

The poll indicates that personal judgments on Barry's job performance are closely linked to public perceptions of his personal honesty. This finding suggests that Barry must deal directly with the integrity issue if he is to recoup politically.

The poll also indicates that Barry is losing ground among blacks of all education and income levels, including less educated blacks who at times have been his strongest supporters.

Barry maintained, however, that he is unfazed by the responses to the question about his political future.

"The public didn't elect me to speculate about what people think in 1990," Barry said. "The public elected me to try to manage the city . . . and I'll spend the next three years and four months of my administration trying to continue to improve the quality of life and reaffirming the faith of those who believe in me."

He added, "If anyone knows about the integrity and honesty of Marion Barry, it's Marion Barry."Washington Post polling analyst Kenneth E. John contributed to this report.