Mayor Walter E. Washington and City Council Chairman Sterling Tucker put aside their political differences yesterday long enough to urge a Senate subcommittee to move ahead on a proposed constitutional amendment that would give D.C. residents full voting representation in both houses of Congress.

Tucker, who announced his candidacy for mayor last Saturday by attacking Washington as "an obstacle to greater home rule," put the blame yesterday on Congress, telling Sen. Birch Bayh (D-Ind.) that "we D.C. residents do not have the power to change the anachronistic rules by which we are governed."

The mayor, who preceded Tucker to the witness table, told the Subcommittee on Constitutional Amendments that "ordinary fairness and basic principles of American democracy require that the citizens of the District have a voice in Congress equal to that of individual citizens across the nation."

Of yesterday's 10 witnesses, only the first, Sen. Dewey Barlett (R-Okla.) spoke against the proposal, but he was the only one among them who will have a vote in the Senate on the resolution which was approved by the House last month by more than the required two-thirds majority.

Joining the mayor and Tucker in urging approval were Del. Walter E Fauntroy, the city's nonvoting representative in the House, Reps. Robert McClory (R-Ill.) and Don Edwards (D-Calif.), three civic leaders and the Australian senator who represents that nation's federal city in its parliament.

The supporters rallied around the theme, as expressed by Fauntroy, that "it is a moral issue," while opponents including two subcommittee members, Sens. William L. Scott (R-Va.) and James Allen (D-Ala.) questioned the constitutionality of the proposal.

Barlett said passage of the resolution would create "a hybrid state" that would force Congress to "sidestep the Constitution" by treating D.C. as a state.

Scott traded sarcastic remarks with Washington and Fanuntroy. He asked the mayor "if it would help your candidacy if I endorsed you" and complained about a city policy that bars employes from traveling on official business to states, such as Virginia, that have not ratified the Equal Rights Amendment. He chided Fauntroy for going to South Carolina in 1972 to campaign against then Rep. John L. McMillan, the long-time chairman of the House District Committee and self-styled "mayor of Washington."

John Hechinger, a former Council chairman; Robert Linowes president of the Metropolitan Washington Board of Trade, and Connie Fortune of the League of Women Voters, repeated the theme that denial of voting representation in Congress to District of Columbia residents is inconsistent with human rights' pronouncements and a 20th century equivalent of "taxation without representation."

John W. Knight, who represents Canberra in the Australian Parliament, testified that none of his nation's states have suffered by extending voting rights to the capital territory.

"It seems to me curious that in this greatest emocratic republic, people in the capital don't have representation in Congress. It's a slightly incongruous situation," said Knight, who came to the hearing at the invitation and expense of Fauntroy.