The Carter administration urged a House subcommittee yesterday to act speedily on a constitutional amendment that would grant the District of Columbia full voting representation in both houses of Congress.

"The administration enthusiastically endorses (the amendment), and considers its enactment a high priority." Assistant Attorney General Patricia Wald told the House Judiciary Subcommittee on Constitutional Rights.

Despite her plea backers of the bill said they have given up hope of House passage before the impending adjournment of Congress, expected later this month and hope to win support for early action next year.

That position was expressed by Del. Walter E. Fauntroy (D-D.C.), the District's present nonvoting member of the House, and by an aide to Rep. Don Edwards (D-Calif.), the subcommittee chairman. The subcommittee may approve the bill before the adjournment, they said.

With yesterday's session, a series of five hearings on the resolution ended. For several weeks, backers anxiously awaited word of the Carter administration's position seeing it as vital to congressional passage. The announcement was made two weeks ago by Vice President Mondale.

For two days this week, Tuesday and yesterday, the subcommittee heard the advice of several lawyers who are reguarded as constitutional experts, and from Wald, who heads the Justice Depaartment's office of legislative affairs.

The principal proposal under consideration would grant the District two seats in the Senate and the same number of seats in the House as any state of similar population - currently two. The proposal would stop short of granting statehood, keeping the city a federal district.

For the most part the testimony was technical, dealing with subtleties of the Constitution and with the question of whether Congress could grant voting representation simply by passing a law or by the more complex method of amending the Constitution.

An amendment requires a two-thirds favorable vote by the House and Senate, and ratification by three-fourths of the state legislatures (37 of the 50 states).

Although there was support for both views, the amendment proposal got the broadest support. Charles Alan Wright, a noted conservative law professor from the University of Texas, said in a written statement that he believes a constitutional amendment is necessary.

Joseph L. Rauh Jr., a Washington liberal lawyer, voiced a generally similar judgement. He contended that opposition to voting representation based upon the near-certainty that the District's lawmakers would be liberals is invalid.

In the Senate and House, he said, the District would elect "like two blacks, likely two Democrats, likely two ultratliberal people. That's what the constituency is here."

Rauh, who is white, modified part of that view a few moments later. "I'd like this to pass before I conk off because I'd like to run for the Senate from the District of Columbia," he said.

Other constitutional lawyers who testified this week were Peter Raven-Hensen, a scholar of D.C. electoral politics; Herbert O. Reid Sr. of the Howard University law school; Arthur S. Miller of the George Washington University National Law center, and Stephen A. Saltzburg of the University of Virginia law school.