Senate Minority Leader Howard H. Baker Jr. (R-Tenn.) annnounced yesterday that he will join with other colleagues Tuesday in supporting a constitutional amendment that would give the District of Columbia full voting representation in Congress.

Baker's announcement continued the momentum for passage of the D.C. voting rights legislation, and several additional key proponents of the measure spent the weekend soliciting further support.

"I expect the resolution to pass; I expect a great number of Republicans will join me . . . ," Baker said during an appearance yesterday on the NBC program "Meet the Press" (WRC-TV).

Baker noted that both national political parties have adopted platforms calling for Washington residents to be [WORD ILLEGIBLE] the right to elect their own senators and representatives. And he said that, once he has taken a position on an issue, "you must assume I am going to try the best I can to take as many Republicans as I can with me."

The news of Baker's support for the voting rights amendment - which has already passed in the House - was greeted with uncontained glee yesterday by Walter E. Fauntroy, the city's nonvoting delegate in Congress.

Watching a rebroadcast of the Baker interview later in the afternoon, Fauntroy, a Democrat, slapped his knee and punched his arm into the air in delight as the Republican leader said he felt that many in his party were prepared to support the voting rights bill.

Fauntroy and others had gathered at the United Methodist Building a block from the Capitol, where a group calling itself the Coalition for Self-Determination has set up a phone bank, staffed by volunteers, to lobby for the amendment's passage.

It takes two-thirds of those present and voting to pass a proposed constitutional amendment. Senate Majority Leader Robert C. Bryd (D-W.Va.) has said that absenteeism could defeat the voting rights bill if Tuesday's balloting is as closed as expected."

Byrd and Sen. Robert Dole (R-Kan.) both said in separate announcements Saturday that they intend to vote in favor of the amendment, whose support in the Senate is being led by Sen. Edward M. Kennedy (D-Mass.).

"I just want to be on the floor of the Senate when the clerk calls the roll," said Fauntroy, who shouted out an "Oh, my goodness," when he heard Baker promise to lobby other senators for the bill's passage.

But Fauntroy and an aide to Kennedy cautioned yesterday that they do not regard the voting rights amendment as a sure thing.

Between 62 and 65 senators are considered likely to vote for the amendment, according to sources and a Washington Post survey. About 26 senators appear to be opposed to the measure. If all 100 senators are present Tuesday, 67 votes would be needed to pass the amendment.

Sen. Orrin G. Hatch (R-Utah), one of those leading the opposition to the voting rights bill, could not be reached for comment yesterday on Baker's support for the measure.

On Saturday, however, when Dole joined the list of voting rights supporters, Hatch said he was disappointed but still thought he and others could round up enough votes to block the amendment.

Hatch and opponents of the bill, much like Fauntroy and the amendment's proponents, have busied themselves calling undecided senators or those senators who they think can be persuaded to switch their positions.

Mayor Walter Washington telephoned some key senators on Friday in what an aide said was an inconclusive effort to get their votes for the amendment. The mayor plans to continue his lobbying up until the vote Tuesday, the aide said.

"I'm not prepared to discuss the prospects for the vote, said Fauntroy, "although I'm obviously more encouraged today than I was yesterday."

Working from what Fauntroy said was a list of 7,000 to 8,000 people in congressional districts across the country, volunteers yesterday were calling such states as Pennsylvania, Alabama and Texas to urge residents there to telegraph their senators in support of the amendment.

"One man I talked to knows (Sen. John J.) Sparkman (D-Ala.) well enough that he's going over to talk to him about it tonight," said John Thompson, a member of the National Association of Real Estate Brokers, who was working as a Coalition for Self-Determination volunteer.

His wife, Virgie, also was at the coalition's "command center" yesterday, attributing her support for the amendment simply: "I'm a native Washingtonian."

Linking the D.C. voting rights issue to the civil rights struggles of the 1960s, Fauntroy said the bipartisan support in the Senate for the D.C. measure was "really a tribute" to the life and work of the Rev. Martin Luther King Jr.

"I used to tell Martin, Dr. King, that we'd never be free in Washington until our people were free to vote in the South," Fauntroy said, recalling long-ago conversations with the slain civil right leader.

But the District's only nonvoting representative in Congress emphasized yesterday that even if the voting rights amendment passes Tuesday "the ratification process will be another hurdle."

United Press International quoted Sen. Patrick Leaht (D-Vt.), chairman of the District Appropriations subcommittee, yesterday as saying the fight to get 38 state legislature to ratify the constitutional amendment within the required seven-year period "is going to make the ERA battle look like a warm-up exercise."