The House took a historic first step toward granting full voting representation in Congress to District of Columbia residents yesterday by approving a proposed constitutional amendment that would give the city two senators and at least one representative.

The 289-127 vote, 11 more than the required two-thirds majority, immediately set in motion a campaign for similar approval in the Senate. Sen Edward M. Kennedy (D-Mass.) released a bipartisan letter, signed by Sen. Barry Goldwater (R-Ariz.) and 16 others, that called for Senate endorsement of "this fundamental principle of justice."

If the resolution passes the Senate by two-thirds majority before the end of this year, it would require ratification by 38 states within seven years before it could take effect.

During the 15-minute voting period in the House, as scoreboards at each end of the chamber tallied the vote, non-voting D.C. Del. Walter E. Fauntroy pumped his arms up-and-down as if he were rooting home a longshot.

When House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) announced the official result at 1:15 p.m., hundreds of boosters who had nearly filled the public gallery stood and applauded and joined most members of the House in celebrating its passage.

Fauntroy, who had been the chief spokesman both on and off the floor, hugged and clapped and cried at the decision. In an emotional speech to his colleagues, Fauntroy said the outcome "reaffirmed my great faith in the American people and you."

As he walked from the lectern, Fauntroy got a bearhug from Rep. Peter J. Rodino (D-N.J.), whose Judiciary Committee had propelled the issue to the floor with an overwhelming 27-to-6 vote on Jan. 31.

Rodino lauded Fauntroy for "leading the fight and expressing the will of the people."

House Majority Leader Jim Wright (D-Tex.) proclaimed it "a great day in ratification process, probably through the history of the District of Columbia, and a great day in the history of human freedom. It asserts the belief that there is no such thing as a second-class citizen in America."

Fauntroy acknowledged "tremendous bipartisan support" in the vote. He singled out for priase Rep. Don Edwards (D-Calif.), whose Subcommittee on constitutional and Civil rights drafted the resolution and guided it through the Judiciary Committee; Tep. Robert McClory (R-Ill.), "who led the Republican effort in committee and on the floor," and Rep. John Buchanan (R-Ala.), who like Fauntroy is an ordained minister.

Fauntroy recalled that Buchanan, a white Republican from Birmingham, "cried with me when we lost two years ago and cried with me today when we won. He is the conscience of the Congress."

The roll call showed that Democrats voted 228 to 48 in favor, and Republicans 61 to 79 against the amendment. Among the representatives whose districts are closest to Washington, only Rep. Marjorie S. Holt (R-Md.) voted no. Supporting the proposal were Reps. Herbert E. Harris (D-Va.) Joseph L. Fisher (D-Va.), Gladys Spellman (D-Md.) and Newton I. Steers (R-Md.).

Before the final vote, the House rejected an amendment, offered by Rep. M. Caldwell Butler (R-Va.) that would have greatly narrowed the scope of the amendment.

Butler sought to limit voting representation for the District to the House only, and to eliminate provisions that call for the city's vote in the electoral college to match its representation in Congress (which would be two senators and one or two representatives, depending upon the 1980 census) and for participation in the constitutional the City Council.

City Council Chairman Sterling Tucker, local coordinator of Self-Determination Coalition for D.C., said Butler's decision to combine his modifications in a single amendment was a tip off that opponents "were not going to fight too hard." During consideration of the resolution by the Judiciary Committee, Butler forced a debate and vote on each part of the modifications through a series of amendments.

In the end, Tucker said, "the rightness of the argument prevailed."

Butler expressed surprise at the outcome, saying "the House expressed itself a good deal more strongly than I had expected. There has been a substantial change in sentiment" since a similar measure fell 45 votes short of the needed two-thirds majority two years ago.The March 1976 vote was 229 to 181.

Butler urged passage of his diluted version as a compromise, "a kite that will fly." The original proposal "goes much too far," he said, predicting it would "bring no additional representation for the District" because it could not be accepted by the Senate.

But after the final vote, Butler said "perhaps my judgment was premature, and not too sound.

The Senate has been viewed as a bigger obstacle than the house because adoption of the amendment would expand membership in "the world's most exclusive club" to 102. Giving the District of Columbia a vote or two in the House would result in a realignment of its constant 435 seats, something that occurs automatically after each decennial census.

A largely subsurface issue is the racial implication of extending voting representation in Congress to a majority black District, but in recent weeks Fauntroy had dealt with the subject in a low-key manner.

At a "newsmakers forum" at the Embassy Row Hotel last month, sponsored by WRC radio, for example Fauntroy said in answer to a question that he hoped no opposition to the measure would be based on the acknowledged likelihood that the city's elected senators and representatives would be "urban and black and Democrats."

Several persons suggested yesterday, however, that race might work in behalf of the amendment's passage in the Senate.

For example, one Senate staffer said that Sen. Strom Thurmond (R-S.C.) "came close" to signing Kennedy's bipartisan letter, and that Thurmond is still considered a likely supporter of the issue.

"Strom has a tough race" for reelection this year," the staffer noted, and the one-time segregationist candidate for president is aware that, unlike previous years, a substantial number of voters in South Carolina are black.

Council Chairman Tucker said he was "hopeful" that Thurmond soon will announce his support for the proposal. A spokesman for Thurmond said only that "Mr. Fauntroy talked to the senator, but he hasn't yet decided" which way to vote.

Dick Clark of Common Cause, who is national coordinator of the Self-Determination for D.C. coalition, said "it's a political reality" that any congressional delegation from the District of Columbia would be comprised of black Democrats. "But anyone who puts that kind of consideration (into the decision of how to vote) wouldn't deserve to be in the Senate. It won't happen," Clark predicted.

If the Senate treats the amendment as a political question, rather than as a moral one, as its supporters are urging, Clark said "the vested interest" of diluting the power of 100 members would more likely be a consideration than race.

In addition to courting Thurmond, Clark said supporters will go after "so-called strict constructionists" such as Sen. James B. Allen (D-Ala.).

"He could make a big difference if he'd make a stand on principle," Clark said.

"It's a good sign," Clark added, that signers of the Kennedy "dear colleague" letter were "not ideologically monolithic."

The other signers were Demoracts Birch Bayh of Indiana, Paul S. Sarbanes of Maryland, Patrick J. Leahy of Vermont, Alan Cranston of California, Thomas F. Eagleton of Missouri, Henry M. Jackson of Washington, Daniel K. Inouye of Hawaii and Abe Ribicoff of Connecticut. Republican signers included Charles McC. Mathias of Maryland, Edward W. Brook of Massachusetts, Lowell P. Weicker Jr. of Connecticut, Jacob K. Javits of New York, Robert T. Stafford of Vermont, John C. Danforth of Missouri, and H. John Heinz III of Pennsylvania.

Tucker, who is Fauntroy's choice for mayor, has been in the limelight throughout the House debate because of his role in the coalition, and not as a candidate, according to Fauntroy's office.

Mayor Walter E. Washington, who was at home with the flu, issued a statement saying he was "elated" by the vote. The "absolutely marvelous effort. . . was another instance where we have been able to get excellent results through a bipartisan local and national effort involving both citizens and officials."

Another mayoral candidate, Councilman Marion Barry, praised "the strong support of President Carter and Vice President Mondale." Barry said "we've come as long way from the years when we could not even get a successful House committee vote on the measure. . . We must work harder than ever until true self-determination is won."

In a separate development, Kennedy said he attempted informally to obtain unanimous consent of the Senate to refer the House-passed amendment to the Senate Judiciary Committee under a 60-day time limit, but said he was blocked when Sen. William L. Scott (R-Va.), would not agree.

Kennedy said he would place the House-passed resolution directly on the Senate calendar, a parliamentary procedure used on major civil rights bills in past years to assure that the full Senate will have a chance to vote on it.

A spokesman for Bayh, who is chairman of the Senate subcommittee on constitutional amendments, said hearings will be held in late April or early May on an identical Senate resolution.

But if the Senate version is blocked in committee, Kennedy's action would permit a vote on the House proposal unless the Senate calendar becomes bogged down by filibusters.