Mayor Marion Barry, bolstered by new support from black voters, has established an early 13-point lead over challenger Patricia Roberts Harris in an essentially two-way battle for the Democratic nomination for mayor, according to a new Washington Post poll.

With the primary 10 weeks away, 45 percent of those interviewed said they now support or lean to Barry, compared to 32 percent for Harris, 5 percent for D.C. City Council member John Ray, 3 percent for council member Charlene Drew Jarvis and 1 percent for physician Morris Harper. Fourteen percent of those interviewed said they were undecided.

The results of the survey of 1,374 Democrats registered to vote in the Sept. 14 primary differed sharply from a late April poll conducted for the Associated Press and WRC-TV (Channel 4) that showed Harris leading. The Post poll was taken by telephone between June 16 and June 22.

The poll shows Barry broadening and reshaping his political base since his election in 1978, when he drew his strongest support from whites, won only four of the city's eight wards and captured the three-way Democratic primary with a scant 35 percent of the vote.

Barry leads Harris in seven of the city's eight wards, and draws strong support among black voters and older citizens, the poll indicated. He also does well among men, city employes and union members.

Among blacks, Barry is the choice of 49 percent, compared to 29 percent for Harris. Among whites, 40 percent were for Harris, compared to 36 percent for Barry.

Barry and his campaign director, Ivanhoe Donaldson, declined to comment on the poll yesterday.

Sharon Pratt Dixon, campaign director for Harris, said the results of the poll were not surprising because Barry is an incumbent running with strong financial backing. "We knew it was a very fluid situation," Dixon said of the Harris campaign. "There was a surge of interest in her candidacy. We knew that surge could not continue on a sustained basis."

Peter Hart, Harris' pollster, said he too was not surprised by the findings of The Post poll, though, he said, he thought Barry's support was "a little high." Hart said he sees the race as 40 to 30, Barry over Harris, at the moment. But in a head-to-head contest, he said, the candidates are in a dead heat.

Ray said his showing in the poll did not match the response he is getting when campaigning. "What the poll says to me," Ray said, "is that there hasn't been any movement by me. When I'm out there in the streets, that's not the reaction I get . . . . The vast number of people I talk to say they don't want Barry or Harris."

Jarvis said she disagreed with the poll's findings because she believes more elderly people and more women should have been included in the sample. "I am gaining more support," she said. "I am raising more money . . . . The sample does not represent the potential voters and so I'm prepared to continue doing just what I'm doing. I'm determined to continue."

In the first days of the survey, council member Betty Ann Kane was a candidate, placing a distant third to Barry and Harris. One poll question asked voters to name their second choice, and when Kane dropped out of the race her support was allocated to the other candidates on that basis. Without that change, Barry had 43 percent and Harris 29.

Dennis Sobin, a publisher who also is seeking the Democratic nomination, was not included in the poll.

The Post poll indicates that Harris leads Barry in only one area of the city, Ward 3, west of Rock Creek Park. Barry carried that predominantly white, affluent ward in the 1978 primary with 47 percent of the vote. But now, the poll found, Harris is the choice of 42 percent, and Barry, 38.

The poll found that Barry has considerable strength in Wards 4 and 5, middle and upper-income black neighborhoods of Northwest and Northeast Washington, which Harris' aides considered a stronghold of her support. Barry leads Harris, 45 percent to 27 percent, in Ward 4, where Harris lives, and 42 percent to 34 percent in Ward 5.

Barry holds a better than 2-to-1 advantage over Harris in Ward 7, where he lives, 55 percent to 21 percent. He runs comfortably ahead of her in Ward 1 (48 percent to 30) and in Ward 2 (45 percent to 31). In Ward 6, Barry leads also, 45 percent to 36 percent, and in Ward 8 as well, 43 percent to 33.

He seems to draw broad support from Democrats of most age, income and education groups. Harris matches or comes closest to Barry in support among voters under 30, middle-income people who earn $15,000 to $30,000 a year and women.

Barry's experience as mayor and his reputation as an advocate of the poor were often cited by his supporters. "He has a better idea of what it's all about for underprivileged," said a 41-year-old black plumber's helper in Ward 8, who said he has lived in Washington all his life.

Barry's supporters were frequently not critical of Harris: "I'm just not sure about her," said a black, 65-year-old telephone interviewer in Ward 4. "I can't picture her in local politics."

Six percent of those who said they support Barry said they disliked Harris because of various personal traits. Pride, arrogance and aggressiveness were cited most often, but only by a total of 17 people.

The main complaint about Harris, volunteered by 13 percent of Barry's supporters, is that she has not been active in the community. "She is an outsider . . . interested in using the mayoralty as a stepping stone," said a 31-year-old Hispanic lawyer who said she lives in Ward 3.

Harris' supporters were generally more critical of Barry than Barry's supporters were in assessing Harris.

"He's not a good manager of the budget," said a 28-year-old black bank worker. "He has a lack of knowledge of who and where to put people to help him. He doesn't have the support he needs to prosper."

Of the Harris supporters, 13 percent were critical of personal traits of Barry, with 15 persons questioning his honesty.

One-third of the Harris supporters complained that Barry was either incompetent or has done a poor job as mayor. In addition, one of every eight Harris backers volunteered specifically that Barry had not kept campaign pledges made in 1978.

"He broke his promises," said a 70-year-old retiree from Ward 4. "He can't even keep the vacant lots clean until election time."

Women voters interviewed said they preferred Barry over Harris by a slim margin of 40 to 34 percent, and a number of Harris supporters, when asked what they like about her, said they liked the fact that she is a woman. By comparison, men favor Barry over Harris, 52 to 30 percent.

Among those who say they voted for Barry in 1978, 58 percent are supporting him now, 25 percent are for Harris and 12 percent are undecided.

Among those who said they supported former council chairman Sterling Tucker in the 1978 mayoral primary, 49 percent said they favor Harris, 27 percent for Barry, 8 percent for Ray, 2 percent for Jarvis and 14 percent undecided.

Of those who said they supported former mayor Walter E. Washington, about 45 percent said they support Barry, 33 percent Harris, 5 percent Ray, 2 percent Jarvis and 15 percent are undecided.

The Post survey suggests that Barry's support is less likely to switch to another candidate than is Harris'. Sixty-nine percent of Barry's backers say they are "strong supporters," while 60 percent of those backing Harris say their support is strong.

Three-fourths of the Democrats interviewed said they are almost certain to vote, and among them, Barry leads Harris 45 to 33 percent.

Included in the poll as Barry supporters are 4 percent who said they have not made up their mind about the election but are leaning to the mayor. Similarly, the 32 percent for Harris includes 4 percent who say their vote is not definite but that they are leaning to her.

Polls done last year and earlier this year for Harris, Barry and other candidates indicated that Barry and Harris were jockeying for the lead, with no more than seven percentage points ever separating them, according to sources who have seen those polls.

More than half the Barry supporters said he has the experience and ability needed to be mayor or that he has done a good job until now. One-quarter praised Barry's handling of particular city programs, such as housing, and one in six of his supporters said he is an active mayor who is involved in city life.

Overall, 17 percent of those polled said they would not vote for Barry under any circumstance, while 8 percent said they felt that way about Harris.

The poll suggests that Harris does best with those who think they know her best. Among voters who said they feel they know a great deal about her, she leads Barry by 48 to 39 percent. But those who said they know Harris well add up to only 13 percent of the voters, according to the survey.

Another 43 percent said they knew "a fair amount" about Harris, and she leads Barry among them by 46 to 38. However, Barry leads by 52 to 21 among those who feel they do not know much about Harris--a group that makes up 25 percent of the electorate. And among the 18 percent who say they know hardly anything about her, Harris trails Barry by 5 to 60 percent.

Of those who said they support Harris, 66 percent cited her experience and ability to do the job, 22 percent cited personal characteristics such as intelligence, aggressiveness and honesty.

Barry shows strength among persons 60 and older, winning 48 percent of the vote to 21 percent for Harris. Similarly, he leads Harris 46 to 29 percent in households where someone is employed by the city government, and 43 to 30 percent in other households.

Those who said they were labor union members favor Barry 47 to 28 percent over Harris while nonmembers favor him by 43 to 30.