President Carter's support for human rights around the world should boost the District of Columbia's renewed attempt to get full voting membership in Congress, Del. Walter E. Fauntroy (D-D.C.) said yesterday at a rally that opened a new drive for representation.

Rep. Don Edwards (D-Calif.) told the Capitol Hill rally that hearings into a proposed constitutional amendment on the subject would begin July 25 before the House Judiciary Subcommittee on Civil and Constitutional Rights, which he heads.

The Judiciary Committee approved identical legislation last year, but it failed to win passage in the House.

The measure would grant the District two senators and two representatives, the same voting strength it would have if it were a state. The city has been represented by a single non-voting delegate, Fauntroy, since 1971.

There would be no change in the city's limited home rule form of local government.

A bipartisan panel of senators and representatives was joined at yesterday's rally in the Rayburn House Office Building by several D.C. political figures. All predicted success and exhorted the audience of about 150 to become the nucleus of a lobbying campaign.

Fauntroy, opening the rally, said Carter's human rights initiatives have brought winds of change in many parts of the world, from the Soviet Union to southern Africa.

"But nowhere does the rhetoric of human rights stir greater hope and expectation than right here among the citizens of our nation's capital," Fauntroy declared, continuing:

". . . Our hope is that the leadership that our President and Congress are giving at long last . . . will bear its first fruits right here" by granting representation.

Although Carter voiced generalized support for congressional voting rights soon after he entered the White House, he never spelled out details of his position.

At a meeting next Tuesday, the White House task force on D.C. problems is scheduled to discuss the representation issue at a closed meeting.

However, that discussion will not be conclusive. Martha (Bunny) Mitchell, the President's liaison on D.C. matters, is expected to listen to the various viewpoints. She will recommend possible presidential positions on this and other matters in a paper she has said she hopes to present to Carter next month.

Mitchell could not be reached for comment yesterday.

When the Judiciary Committee last year approved identical legislation to that now pending, it lacked support from the Ford administration.

When nose counts showed it was doomed to defeat, a substitute was offered that would have granted the District only a single vote in the House. That fell 42 votes short of the necessary two-thirds majority in the House. It never got to the Senate.

Fauntroy told a reporter yesterday that preliminary counts show the full voting measure "has a good chance in the House and a fighting chance in Senate." Many senators are reported to be resisting an enlargement of that chamber's membership of 100.

"We'll get it through the House; we'll get it through the Senate," predicted Sen. Edward W. Brooke (R-Mass.). "I was born here (in Washington)," Brooke added. "I had to leave here to run for the Senate."

Even if it is approved by Congress, the measure still must be ratified by 37 state legislatures, or two-thirds of the total.

Other lawmakers who attended the rally included Sens. Charles McC. Mathias Jr. (R-Md.) and Edward M. Kennedy (D-Mass.) and Reps. John A. Buchanan (R-Ala.), Ronald V. Dellums (D-Calif.) and Robert J. McClory (R-Ill.), D. C. Mayor Walter E. Washington, City Council Chairman Sterling Tucker and members of both the Council and the Board of Education also attended.

Yesterday's rally was organized by Self-Determination for D.C., a coalition of more than 50 local and national organizations. It occupies space in the office of Common Cause, a citizens' lobby, at 2030 M St. NW.