Third Ward Democrat Polly Shackleton announced her plans to seek reelection to the D.C. City Council yesterday, saying she intends to "run on my record and if elected will continue to give highest priority to responsive government."

Shackleton's announcement was made outside the council chambers at the District Building and made her the first of seven council members whose terms expire this year to announce plans to seek reelection to the same post this fall.

"I feel it's very, very important to have continuity (in city government)," Shackleton said. "We have a lot of problems in this city, but we are making progress."

Shackleton, 67, is a long-time city Democrat, former Democratic National Committeewoman, and civic activist who served on the city's first appointed council, which was established in 1967. She was the overwhelming winner of the 1974 Democratic primary in Ward 3, which is comprised mostly of neighborhoods west of Rock Creek Park. She went on to win election to a four-year term by winning the general election by a near 5-3 margin over her closest opponent, Republican Albert A. Rosenfield.

At present, Shackleton faces no anounced opposition. Her strongest likely challenge is expected to come from Ward 3 school board member Carol L. Schwartz, a Republican. About one-fourth of the voters in the mostly white, upper-income ward are Republicans.

But Schwartz said recently that she does not plan to un against Shackleton. The two people who were Shackleton's strongest opponents in the 1974 Democratic primary - Kay Campbell McGrath and Mary Lela Sherburne - are among more than 200 persons listed as members of the committees supporting Shackleton.

In her three years on the elected council, Shackleton has been chairwoman of the Committee on Human Resources and Aging, and at times was one of the principal critics of former D.C. Department of Human Resources Director Joseph P. Yeldell.

Most of her council colleagues give her high marks for constituent service and neighborhood involvement.she surprised some city hall observers last year when she voted against start-up funds for a proposed $110 million convention center near Mt. Vernon Square in downtown Washington.

Shackleton has generally been a close associate of council member Marion Barry (D-at large) who is running for mayor this year. Yesterday, however, Shackleton refused to endorse either Barry or the other council member running for mayor, Council Chairman Sterling Tucker. She said only that she felt there were "two fine candidates for mayor."

That apparent neutrality was partially explained by the fact that the supporters of both Barry and Tucker were among those on Shackleton's list of backers. Chuck Clinton, chairman of an umbrella group of civic organizations known as the Wisconsin Ave. Corridor Committee, will run the Shackleton campaign. Daniel H. Crowley, a lawyer, will be treasurer and finance chairman.

The Democratic primary is Sept. 12 and the general election is Nov. 7. In addition to Tucker and Shackleton, the only other candidate whose term expires this year who has announced political plans is council member Douglas E. Moore (D-at large), who is running for chairman.