The Senate beat a strategic retreat in the face of widespread day not to contest an unusual House decision to reject $54 million for a new Senate office building.

But sufficient funds already have been appropriated to keep the Philip A. Hart Senate Office Building under construction for the foreseeable future.

And Sen. Warren Magnuson (D-Wash.), chairman of the Senate Appropriations Committee, said it is likely that additional funds will be sought next year to complete the project, which has encountered a series of substantial cost overruns.

Magnuson commented shortly before the Senate voted 61 to 11 to approve the House-Senate conference report on the $6.8 billion supplemental appropriations bill, which contains additional financing for a number of federal agencies.

The money for the Hart building originally was added to the bill on the Senate floor after critics of the structure's cost and frills failed in an attempt to stop work entirely and convert the building site into a parking lot.

But the House, in a rare incursion into the Senate's traditional domain, eliminated the new funds for the building in the bill as well as a $135 million spending eeiling that the Senate had imposed on the project.

Although the House action triggered outbursts in the Senate, it was decided not to contest the cut, mostly on grounds the money is not needed immediately and that it will be exceedingly difficult to stop construction after the $85 million now available has been spent.

Some of the design features of the new building that have received the most critical attention include a soaring and skylighted marble atrium, a gymnasium and a rooftop, senators-only restaurant.

Several senators, including Russell B. Long (D-La.) and Jennings Randolph (D-W.Va.), rose to defend the building, which has been denounced by critics as "Mussolini style," a marble palace" and "an American Taj Mahal."

Supporters said the building is essential to meet the space needs of a rapidly growing Senate staff.

But Sen Richard G. Lugar (R-Ind), said the main reason the House had intruded into what normally would have been considered the Senate's business was that members "had been hearing from their consitituents that all things considered they would prefer to have the building stopped."