David A. Clarke, who two weeks ago cited "growing racial distrust" in Washington as one of the reasons he would not run for chairman of the D.C. City Council, reversed himself yesterday and said he will seek the Democratic nomination for the post in the Sept. 14 primary election.

"At the time, I thought it was the right thing to do," Clarke, a two-term liberal Democrat from Ward 1, said of his April 8 decision to pass up the chairman's race and instead run for an at-large seat on the council. "I have received a number of equally sincere communications from persons who thought I was wrong," Clarke said.

Clarke, who is white, had said he was reluctant to run against incumbent Arrington Dixon, who is black, because the poor economy and the policies of the Reagan administration had aggravated racial relations in the country and in Washington, where the population is about 70 percent black.

"I have been sensitive to that and I continue to be," Clarke said, seated next to his wife Carole at a District Building press conference yesterday. However, he said, he was "mildly chastised" by some callers--whom he did not identify--for bowing to what he saw as racial tensions rather than trying to correct them.

"After some serious reconsideration and noting that no other council member has become a candidate," Clarke said yesterday, "I have concluded that it is far better for the city to have a campaign in which the issues are aired, albeit possibly obscured, than for the issues not to be raised at all."

"For some people race will continue to be an issue," Clarke said. "And I think it is better for those for whom it is an issue that it be talked about as such. And I certainly think I have tried to be candid. Frankly, if you have an issue like that you have to talk about it."

Clarke's action yesterday made him the only announced candidate opposing Dixon, elected chairman in 1978, who has formally launched a reelection campaign and already raised $40,000.

At his own press conference yesterday, Dixon said he did not share Clarke's view of racial tension in the city, adding, "I would be concerned about any suggestion . . . that there is any polarization in the city.

"I have lived here all my life. I have never encountered it," Dixon said. "I think competent people will be elected."

Clarke said in his April 8 announcement that a private poll he had commissioned in February had indicated that as much as 20 percent of the voters in Ward 4--a mostly black, middle-class area of upper Northwest that traditionally has a heavy voter turnout and which Dixon represented before he was elected chairman--would not vote for a white person for chairman.

Clarke, who easily won reelection in his predominantly black and Hispanic ward in 1978, said race has "been a factor in my ward. It has been a matter that I have frankly discussed with my constituents."

But he said "in an election year in which the mayor's campaign is the dominating matter of attention, that kind of communication might not be effective."

Clarke said he decided last week that he should challenge Dixon but delayed his announcement until yesterday to give council member John A. Wilson (D-Ward 2), who officially pulled out of the mayor's race on Monday, a chance to get into the campaign for chairman. Wilson, who is black, did not.

Clarke, who at one point last month filed formal papers to run against Dixon but retrieved them a short time later, acknowledged at yesterday's news conference that indecisiveness may have cost him political momentum.

The 38-year-old Howard University Law School graduate has spent several months courting Mayor Marion Barry. Yesterday Clarke said that Barry had told him that Barry would not endorse anyone in the chairman's race but would say publicly that he opposes Dixon's reelection.

Barry, however, refused later in the day to say anything to reporters about the chairman's race. Clarke, clearly surprised, said, "I stand by what I said." After consulting with Barry, Clarke said Barry told him that the mayor's remarks about the chairman's race should be considered "private."

Clarke said he would wage his campaign on contentions that Dixon has failed to support or take a leadership role on several major issues involving poor and middle-income people--including rent control, displacement of residents, city supplements to cuts in federal welfare programs and crime legislation.

Dixon said at his press conference that he would campaign on his record. "I'm prepared to go to the public about my record," Dixon said. "I represent the people of the city. I belong to every special interest group in the city."