Speaking on the eve of a crucial House committee vote, Vice President Mondale urged national civil rights leaders yesterday to help the District of Columbia win voting representation in Congress.

"There is no excuse for denying more than 700,000 Americans full representation in Congress because they live in the Nation's Capital," Mondale told the Leadership Conference on Civil Rights, composed of top officials of rights organizations.

Washington residents have never had voting representation, which Mondale declared was "a blot on our record of human rights."

Mondale, who is the chairman of a White House task force on District of Columbia problems, said today's vote by the House Judiciary Committee on a constitutional amendment to grant full representation is crucial.

The measure would grant the same voting membership in both the Senate and House that the District would have if it were a style - two senators and either one or two representatives, depending on a complex mathematical formula based on both national and local population. However, there would be no change in the District's limited home rule form of local government.

To go into effect, the measure must be approved by two-thirds of the members of both houses of Congress and ratified by three-quarters, or 38, of the 50 state legislatures.

At present, the District is represented in Congress by only a nonvoting delegate, Walter E. Fauntroy (D), who has held the post since it was created in 1971.

Rep. Don Edwards (D-Calif.), the manager of the pending measure and a cosponsor of it with Fauntroy, predicted that the 34-member Judiciary Committee will approve it today by a margin of better than two to one.

If any amendments are proposed to weaken the measure, Edwards said, "we're going to fight them off."

This year's effort is the second attempt to win congressional approval for the measure.

Two years ago a majority of House members supported a measure that was diluted at the last minute in an attempt to win passage. But the tally, 229 to 181, fell 45 votes short of the two-thirds needed for passage. The measure never reached the Senate.

Banking on stronger support this year from the House leadership, Edwards and Fauntroy have predicted victory when the measure reaches the floor.

The Senate, with its smaller membership of 100 and its clubby atmosphere, is regarded as a tougher obstacle. Senate supporters have said the measure has a fighting chance there.

A public campaign and lobbying effort to win passage of the measure have been coordinated by a coalition of 52 local and national organizations that calls itself Self-Determination for D.C.

It includes such groups as the League of Women voters, the citizen lobby Common Cause and a long list of labor unions, civil rights groups and religious organizations.

Littel has been heard of the coalition locally, since it has used most of its resources trying to muster support around the nation, hoping to influence members of Congress who must vote on the issue.

Elena Hess, secretary of the coalition, said one method has been telephone calls on Sundays, using WATS (wide area telephone service) lines provided by Common Cause D.C. City Council member David A. Clarke spent part of a day making such calls.