Senate leaders agreed yesterday to allow the full Senate to vote Tuesday on a constitutional amendment that would give District of Columbia residents the right to select their own senators and representatives, ending a day-long filibuster against the bill.

Despite the suddeness of the filibuster's collapse, the bill's backers were emphasizing yesterday that the amendment's fate in Tuesday's vote still hung in doubt.

Nonetheless, after almost a century of lobbying and congressional rebuffs, the question of whether District of Columbia citizens are entitled to the same voting representation in Congress as residents of the nation's 50 states will get its most definitive hearing yet. The House already has approved the constitutional amendment.

Even if the bill wins the required 67 votes in the Senate on Tuesday, still it must be approved by the legislatures of 38 states within the next seven years before it becomes law.

Supporters of the bill regarded yesterday's agreement as a victory because it avoided the necessity of a cloture vote today to kill an on-going filibuster against the bill. While supporters said they had the 60 voters needed to cut off debate that had threatened to fatally stall the bill, a potentially dangerous confrontation between you pro and antibill forces was avoided.

"It's a great thing they've done to allow the issue to come up for a vote up or down," said an aide to Sen. Edward M. Kennedy (D-Mass.), the floor manager for the constitutional amendment.

One aide to a senator who opposes the constitutional amendment said late yesterday that the reason the opposition agreed to the Tuesday vote was because they were confident they had the votes to defeat the measure.

"If you have the votes, you don't need to continue the filibuster," the aide said.

Yesterday's agreement was hammered out by Senate Majority Leader Robert C. Byrd (D-W.Va.) in consultation with one of the bill's opponents, Sen. William Scott (D-Va.) in an attempt, Byrd said, to save the Senate time and to ensure a certain up-or-down vote.

Byrd said that the agreement had been necessary because, even if cloture had invoked successfully every senator would have had the right to speak for an hour on the measure and to introduce an unlimited number of amendments at the same time.

Our opposition crumbled," said on aide to Sen. James A. McClure (R-Idaho), organizer of the filibuster, yesterday. The aide said that he was very puzzled and surprised by the action.

Under the terms of the agreement, McClure will be allowed to offer seven amendments to modify the amendment on Tuesday. The aide said that McClure will indeed after amendments, including one that would cede back to Maryland those portions of the District of Columbia that are not owned by the federal government.

The District of Columbia was carved out of Maryland in the late 1790s when Congress chose the site for the capital of then-new United States. Even so, Maryland's two senators were not eager to see the city reintegreted into Maryland as they led yesterday's successful fight to table a similar amendment offered by Sen. John Melcher (D-Mont.) The amendment was defeated 58 to 33.

"It lacks inherent logical consistency," Sen. Paul Saribanes (D-Md.) said drily yesterday.

McClure and Melcher and several other Western senators began filibustering the bill Thursday, on grounds that it was unconstitutional, immediately after it was introduced by Byrd.

Elena Hess, executive director of Self Determination for D.C., a national coalition working for the amendment's passage, speculated ysterday that supporters moved for the agreement fearing they did not have the votes necessary to end the filibuster.

"They were worried awhile ago that there were not enough people in town to vote," she said. But through constant all-day lobbying efforts the total was "hovering between 60 and 65," she said.

Sixty votes are needed to end a filibuster.

Throughout the day, Kennedy had been active both on and off the Senate floor, quietly urging his colleagues to attend today's vow-aborted cloture session.

At one point during Kennedy's campaign to secure the needed cloture votes, Sen. William D. Hataway (D-Maine) glanced over at Kennedy while both were on the Senate floor and waved his arms in imitation of an airplane and smiled Kennedy point a finger at Hataway and made it clear that he wanted the Maine senator on the Senate floor come Friday and not off in an airplane.

Across the street from the Capitol, members of the coalition for D.C. Self-Determination had set up a command center. Throughout the day they telephoned senatorial offices checking to insure that the bill's allies would be on the floor today.

The amendment's supporters had believed that it would be crucial to defeat the filibuster today if the measure was to survive.

Byrd, whose deft parliamentary tactics were responsible for the bill's introduction Thursday had said yesterday before the agreement on Tuesday vote was reached that the Senate faced, a heavy legislative schedule over the remaining month-and-a-half. As a result, he said, if the cloture had failed today. "I may not put another cloture petition in."

"We can only take so much filibuster," Byrd had said, referring to the number of filibusters the Senate has sustained this year.

Byrd noted that Kennedy had told him that only one cloture vote would be necessary to end the filibuster.

The city currently has a nonvoting delegate in the House.

The proposed amendment passed the House in March and if passed by te Senate, then three-fourths of the nation's state legislatures must ratify it within seven years to make it part of the constitution.