The leadership of both houses of Congress has approved a compromise plan for extending the historic west front of the Capitol at a cost of $55 million, renewing an old controversy between preservationists and construction engineers.

Capitol Architect George M. White, acting on previously undisclosed instructions by the top-level congressional Commission for the Extension of the Capitol, asked a Senate panel yesterday to provide funds for the project, which would take three years to complete.

The project calls for erecting a new marble wall ranging from 19 to about 60 feet outside the existing sandstone facade of the center of the Capitol, some of which dates from 1800 and is the oldest visible part of the building's exterior.

The west front is the facade of the Capitol that is seen from the Mall and downtown Washington. The east front, site of the presidential inaugurations was rebuilt between 1958 and 1961.

Engineers have warned since the 1950s that the old facade is deteriorating bady. Parts of it have been shored up by heavy timbers.

Past proposals for a more ambitious extension have sparked repeated congressional controversies, most recently in 1973 when the Senate Appropriations Committee rejected a $58-million outlay.

Those earlier proposals were advanced as much to gain more space for congressional offices and restaurants as they were to solve the structural problems.

White, testfying yesterday before the Senate Legislative Appropriations Subcommittee, stressed that his new proposal is intended mainly to deal with the structural problems.

He contended that the extension is far preferable to an alternative proposal to drill 5,700 small holes in the Capitol facade to pump in a wall-strengthening cement grout. This would cost an estimated $45 million.

"If we were just doing this for space, I think we would look for some other solution," White told the subcommittee. "The space is a dividend."

He acknowledged that the project would expand the Capitol's floor space by about 25 per cent, providing prestigious hideaways with magnificient panoramic vistas for key lawmakers, as well as more work space for lawmakers close to the two legislative chambers.

Although White did not suggest what use the additional space should be put to, he said there is a severe shortage of "cloakroom" space where House members can meet with constituents.

The earlier extension plans called for adding up to 80 feet to the front of the building, requiring the removal and reconstruction of broad terraces designed by famed landscape architect Frederick Law Olmsted and built between 1884 and 1892.

The Commission for the Extension of the Capitol, which includes Vice President Mondale, who is the presiding officer of the Senate, and House Speaker Thomas P. O'Neill (D-Mass.), approved the new plan at an unannounced meeting April 7. The majority and minority leaders of both congressional chambers also serve on the commission, as does White.

Despite the high-powered support, the proposal already has aroused controversy, leading the chairman of the appropriations subcommittee, Sen. Walter Huddleston (D-Ky.), to rue his role as the man in the middle. "It makes me wonder . . . why me?" he asked rhetorically at yesterday's hearing.

Sen. Ernest F. Hollings (D-S.C.), who blocked the 1973 expansion plan when serving in the post Huddleston now holds, said through a spokesman yesterday that he opposes the new plan as well. Holdings still serves on the Appropriations Committee.

The chairman of an American Institute of Architects task force on the Captiol, Robert Burley of Waitsfield, Vt., testified yesterday against the project. Burley as the architect for restoration of the Vermont statehouse, built in the 1820s.

Conceding that the new Capitol plan looks better than the old one, Burley said "any extension or concealing of the west front would be detrimental in terms of historical significance, architectural integrity, the public image and the symbolic impact for our nation's single most important building."

Visually Burley said the construction project would flatten the facade of the building, a point contested by White, who contended that it would look much the same as it does now when viewed from the Mall.

The project was supported by the National Society of Professional Engineers whose vice president, Sammie F. Lee, said the best solution to the Captiol's structural problem is to build the new wall.

"The present condition is dangerous and may conceivably get worse," Lee said. "There is no controversy, I believe, over the seriousness of the problems with the wall."

White, who devised the new plan himself, was fervent in his support at yesterday's hearing.

"This building was not designed as a single composition," White said. "It grew as the country grew."

As huddleston and Sen. Richard F. Schweiker (R-Pa.) looked on with obvious fascination. White assembled a small scale model of the Capitol that showed how it was expanded from the start of construction in 1793, the completion of the central rotunda with a low dome in 1829, the addition of the existing House and Senate wings between 1851 and 1863 and its topping with the existing huge dome during the Civil War.

"To say that the Capitol, a building that evolved over many years, ought not to be completed in accordance with (a) plan, is a rather negative approach to historic preservation, in my judgment," White said.