D.C. Council member David A. Clarke, after months of indecision, yesterday abandoned plans to run for chairman of the City Council. He said a recent poll he commissioned indicated that his bid would be hampered by low name recognition and "an unfortunate, but growing racial distrust" of a white candidate.

The 38-year-old liberal Democrat and former civil rights lawyer from Ward 1 in Northwest Washington, who is white, said he would seek an at-large seat on the Council, leaving the incumbent chairman, Arrington Dixon, unopposed, as of now, in the Sept. 14 Democratic primary. Dixon is black.

For months, Clarke has been trying to lay the groundwork for a challenge to Dixon. He met with Mayor Marion Barry, who over the past several months has feuded with Dixon. He attended community meetings throughout the city, and he calculated the cost of such a campaign and pegged it at $200,000.

At one point about two weeks ago, Clarke filed formal papers to run against Dixon but retrieved them a short time later.

Clarke said yesterday that a poll taken in February indicated that as much as 20 percent of the voters in the city's largest Democratic ward -- Ward 4, a predominantly black, middle-class area in upper Northwest Washington -- "would not vote for a white candidate for chairman." Clarke declined to release copies of the poll's findings.

"I was willing to run if the issue could have been the leadership of the council," Clarke said yesterday. "But it wasn't." He said he feared that the campaign would have been distorted by racial concerns.

"Over the past year, there has grown a distrust among our citizens which is aggravated by the character of the current national government," Clarke said in a two-page, single-spaced statement. "Reaganomics and Reaganism have caused a great division to develop in our nation."

Yesterday, Clarke informed his staff of his decision, then relayed the information to reporters and to Barry.

One factor in his decision, he said, was lack of name recognition outside the area he has represented on the council since 1975, which includes the Mount Pleasant, Adams-Morgan, Cardozo and LeDroit Park neighborhoods.

Another factor, Clarke said, was that he felt the campaign for the chairmanship would "play second fiddle" to the race for mayor.

The impact of race on his campaign prospects was ironic because Clarke has a background and general record on the council supportive of blacks.

A graduate of Howard University Law School, he is a former civil rights activist and former counsel for the Southern Christian Leadership Conference in Washington in the early 70s.

The ward he represents includes several neighborhoods that largely are black and Hispanic. When he was first elected to the council in 1974, the majority of the ward's voters were black.

Running for reelection in 1978, Clarke faced what was first expected to be a strong challenge from a black former civil rights activist, Frank Smith. Clarke easily won the primary easily.

Smith, who subsequently was elected the ward's representative on the Board of Education, now is mentioned as a possible successor to Clarke along with Marie Nahikian, a housing activist who in 1978 ran unsuccessfully for an at-large seat on the City Council.

In this fall's contest, Clarke would be running for the at-large seat now held by fellow Democrat Betty Ann Kane, who is running for mayor and who reaffirmed yesterday that Clarke's decision would in no way affect her plans to stay in the race for mayor.

Kane, who is white, has said polls she had taken last year found that voters in the city, whose population is 70 percent black, did not believe that the mayor had to be black to be effective.

Clarke said yesterday that his race for Kane's at-large seat would not pose the same black-white problem he saw in a campaign for chairman because there is no black incumbent.

"I would not be displacing a black. Maybe that's the way it should be," Clarke said. "I've never before run against a black person to displace one. I've been sensitive to that in the civil rights movement and in the community."