Cutting into the ranks of undecided voters and taking some supporters from his rivals, Mayor Walter E. Washington's late-blooming campaing has catapulted him into a neck-and-neck race with City Council Chairman Sterling Tucker as the Democratic campaign for mayor enters the crucial final week, according to a Washington Post poll.

The poll of 762 registered Democratic voters, taken last Sunday through Thursday, indicates that the contest is still a close one among Washington, Tucker and City Council member Marion Barry.

Overall, neither Tucker nor Barry has lost any ground, but Washington appears to be surging upward, having increased by nearly one-third his share of the vote in the last three months.

As a result, with nine days left before the Sept. 12 primary, Tucker and Washington are fighting for the lead, with Barry close - but decidely - behind, the poll indicates.

In the contest for the Democratic nomination for City Council chairman, the poll found council member Arrington Dixon maintaining a more than 2-to-1 lead over maverick council member Douglas E. Moore.

All 762 persons interviewed last week were among 1,020 registered Democrats surveyed in an earlier Post poll, conducted June 1 through 5. The second poll therefore traces actual change among those who were interviewed.

hose interviewed a second time represent a close but exact duplication of the original sample. A lightly higher proportion of voters who supported Washington in June was included the second time, meaning that overall support for him may be slightyly over-represented.

Among these interviewed, the number in favor of our leaning toward Washington increased from 24.0 percent to 30.8 percent. Support for Barry was basically unchanged - moving from 23.2 percent to 23.5 percent. Tucker's support also was stationary, rising from 30.8 percent in June to 31.4 percent last week.

The undecided vote dropped from [WORD ILLEGIBLE] percent in June to 12 percent. Two percent of those interviewed last week supported other candidates in the mayoral race as compared to 3 percent in June.

In the council chairman contest, Dixon held 60 percent of those interviewed, and Moore slipped from 25 percent in June to 24 percent last week. John G. Martin, who was not included in the June poll, was the choice of 3 percent of those questioned last week.

For the mayoral candiates, who took advantage of yesterday's mild add sunny-weather by plunging into face-to-face campaigning in the streets, reaction was varied.

A jovial but footsore Washington, who had pumped hands at eight shopping centers during the early afternoon, said, when informed of the poll results, "I'm about to do eight more from what you're telling me."

Washington said the poll was interesting" and confirmed "our findings" in street canvassing and telephone interviews "that we're moving up and ahead. I'm confident from that I hear out here and from what I get from you that I'm gonna win."

But, Washington quickly added, repeating what has been able his sole comment on other less optimistic polls, "The only poll that counts is the one taken by the voters on election day."

Barry, calling from a telephone booth on Capitol Hill where he was campaigning, said he did not believe that his campaign was "on hold."

He said the poll's sample of voters, all of whom voted in at least one past election, was stacked against him. "These are hard-core voters that I know I'd have trouble with. My best [WORD ILLEGIBLE] is with voters 18 to 45 who in the past have not voted," Barry said.

Barry accused Washington, Tucker add Del. Walter E. Fauntroy (D-D.C.) of outspending and "ganging up" on him.

"I'm just really happy that they haven't knocked me out of the boxx, with all this money they're spending," he said.

"I should have slipped down seven or eight points by now with all that heavy weight against me. I interpret the holding position as a positive position because any other candidate would have been knocked out."

Tucker, who has been claiming that there is no need to waste anti-Walter Washington votes on Marion Barry, had only a short response while shaking hands along the tree-lined streets of Northeast Washington.

"From the beginning, I knew Washington was my principal opponent," Tucker said, "It's clear now that I'm the only candidate who can produce the change the people want. Clearly, a vote for Barry is a vote for Walter Washington."

The poll indicated that Washington is making his sharpest gains in two unusually key voter-rich and high-turnout wards - Ward 5, most of Northeast Washington west of the Anacostia River, and Ward 7, far Northeast and Southeast Washington - and in Ward 8, the Anacostia section of Southeast Washington that has been often shunned by vote seekers because of its low voter turnout.

The poll indicated that in Ward 3, the largely white and affluent area of the city west of Rock Creek Park, Tucker is gaining on Barry, who still leads there. Washington also has gained support in Ward 3, but is far behind the others.

Two of the most important areas in the final nine days of campaigning could be wards 4 and 5, according to the poll. Both have traditionally been key because they have the highest numbers of registered Democratic voters in the city and also have records of high voter turnout.

Both these wards, according to The Post poll, have relatively high proportions of voters who still have not yet decided on whom they will support for mayor.

While all of the candidates are trading supporters, it is Washington who is holding on best to those who supported him previously. More than 80 percent of those who selected him in June continue to do so now, as opposed to 70 percent each for Tucker and Barry.

The poll also found that Washington has begun to turn around some of the voters who in June indicated that under no circumstances would they support him for relection.

Moreover, he appears to have a decided advantage among those who are still undecided because a significant number of those persons are 61 years of age and older and make less than $10,000 a year. Persons in those categories are among Washington's stronger supporters.

Washington also has made sharp gains among voters in families in which one or more members hold city jobs - a large voting bloc in Washington. Among those interviewed in June and again last week, Washington rose from 28 percent to 35 percent, and Tucker dropped from 35 percent to 32 percent.

The poll suggests that The Washington Post's editorial endorsement of Barry last Wednesday may have had some impact among white voters, but very little, if any, among blacks.

Since the poll was roughly two-thirds complete when the endorsement appeared, it is difficult to gauge its impact.

Before the endorsement, Barry was picking up 37 percent of the support of whites interviewed, Afterward, that figure rose to 50 percent. However, there was no immediate way of determining whether the latter group might have been more disposed to support Barry anyway.

Washington also may have reaped a slight gain from The Post endorsement of Barry. After the endorsement Washington appeared to gain more support from persons who identified themselves as political conservatives.

Barry continued to be the favored candidate among white voters, but Tucker significantly narrowed the gap. Both are far ahead of Washington among white voters. Among blacks, Washington appeared to overtake Tucker as the favored candidate, while Barry remained a distant third.

As the election approaches its final stages, voters appear to hold all three candidates in fairly high regard, both personally and in terms of competence on the job. The poll asked those interviewed to rate the candidates from zero to 10 in both areas. Only 20 percent voted any candidate unfavorably in either area.

Tucker was rated highest for competence with an average score of 7.0, followed by Washington (6.4) and Barry (6.1). Washington was rated highest for his standard of personal behavior and integrity at 7.8, followed by Tucker (7.3) and Barry (6.4).

"Integrity to me is very, very significant as a factor," Washington said yesterday. "If you've got people believing that you've got integrity in government, that is a great margin of victory."