Still exhilarated by his biggest political victory - winning congressional approval of voting representation for the District of Columbia - Del. Walter E. Fauntroy moved yesterday to "use that momentum to help City Council Chairman Sterling Tucker become the city's next mayor.

With the same zeal he used to create a "coalition of conscience" to get the voting representation constitutional amendment passed in the Senate Tuesday, Fauntroy said his next mission is to form a "partnership for change" through his own almost certain reelection and the election of Tucker as mayor and City Councilman Arrington Dixon as council chairman.

Firmly entrenched as the city's nonvoting delegate in the House of Representatives and facing only token opposition in the Nov. 7 election, Fauntroy said he would campaign actively with Tucker as well as by himself. "I'm hopeful that whatever I add (to Tucker's) campaign will be just the margin that is needed to bring about the change that most people want."

Fauntroy has already been broadcasting radio advertisements calling for the "partnership for change" and said that in the last week before the Sept. 12 Democratic mayoral primary his ads will specifically call for the election of a Fauntroy-Tucker-Dixon team. He has also taped television ads for Tucker.

In addition, Tucker campaign aides say that their campaign has largely been meshed with Fauntroy's political organization, one of the most succesful in the short history of elective politics in the District. Fauntroy said he especially will campaign in areas of the city where he is most popular, such as the Shaw neighborhood and the 14th Street and H Street corridors.

In a two-hour interview in his Capitol Hill office, Fauntroy said that the same "kind of teamwork" that led to the amendment's passage would result if Tucker is elected.

"The [House] delegate cannot do much for the city unless he's well coordinated with the city government," Fauntroy said. "I have not been able to effect that kind of partnership with the mayor. The mayor plays sand lot ball in the major leagues."

Fauntroy has attacked Mayor Walter E. Washington, a long standing political foe, on numerous occasions, but his barbs yesterday seemed more pointed than usual.

Fauntroy credited Tucker, the president of the umbrella organization lobbying for the amendment, with an extensive role in winning its passage.

Fauntroy last night took Tucker along with him to Sacramento, Calif., to help persuade California legislature to become the state to ratify the voting rights amendment.

Asked about Washington's role in the passage of the amendment, Fauntroy replied: "Some people have worked very hard. Some people have tried to create the impression that they did."

Judy Rogers, the mayor's legislative assistant, said that the mayor wrote all 100 senators urging passage of the amendment and convened numerous meetings with national groups over the last few years and urged their members to get their congressional representatives to vote for it. Moreover, she said the mayor lobbied senators at the behest of Fauntroy's office.

"This is one instance that was not a petty political issue," Rogers said, adding that the mayor helped sway several senators to vote for the amendment. She said, however, that it "wouldn't be very productive to name anyone."

Tucker also accused the mayor of trying to "elbow in" on the credit for passage of the amendment after allegedly not working for it. The City Council chairman accused the mayor of telling the Redskins welcoming luncheon on Monday that he had to leave to go lobby for the amendment and then going home instead.

Sam Eastman, the mayor's spokesman, said Tucker was mistaken. The mayor's chauffeur dropped the mayor off at his office to make telephones calls to Senators for the amendment and then went to the mayor's home to retrieve some papers, Eastman said.

Fauntroy, who on the campaign trail often exhibits the flair for political theatrics that Tucker at times lacks, said he "sincerely believes" that Tucker is the "best person for managing the District government in a fashion so that we won't be embarrassed as we have been on many occasions and in a fashion that will command the respect of many of the colleagues that I must influence on the Hill."

Fauntroy said he is convinced that a large majority of the District's voters want a new mayor, but said he was fearful that Washington could win again as "a divided majority" splits its anti-Washington votes between Tucker and the other major candidate in the primary, Councilman Marion Barry.

Fauntroy said he has proved that even without a vote in Congress he can help push through important legislation for the District by "mastering the arithmetic of our (black) political power."

He said that by winning the support of such groups as the League of Women Voters, the Leadership Conference on Civil Rights, Common Cause and that of locally elected black officials he has been able to push through legislation giving the District limited home rule, to help maintain federally financed community action programs for the poor and to win Congressional approval of the D.C. voting rights amendment.

While saying that his most recent victory had not quite sunk in yet, Fauntroy said he felt "a tremendous sense of satisfaction because the plan which I announced on seeking this office was ridiculed by people I felt should have known better.

"I have never doubted that with skill and purity of heart and approach the mastering of this arithmetic could be effected," he said. "I used to think I had a peculiar kind of brilliance. I realized the only way to influence members of Congress is to influence them through their constituents.

"I have been annoyed on numerous occasions when people have suggested that my efforts to achieve (passage of the D.C. voting rights amendment) were borne by my naivete," he said.

But he said that with the letter-writing campaign from blacks as well as whites to congressional representatives, the tide began to shift in his favor. Congressmen and senators realized they needed the support from blacks in future elections that now were telling them to support for the D.C. voting rights amendments.

"I hope it makes believers of many people that change can occur," Fauntroy said. "We appealed to their sense of fair play and justice."