A $170-million proposal for a sprawling new Government Printing Office building in North-east Washington received a major boost yesterday as President Carter gave his support for the long-debated undertaking.

The proposed GPO plant is expected to be the most expensive government building ever constructed. Its high cost was attributed by federal officials yesterday partly to continuing inflation and to building's enormous size.

As currently planned, the new GPO headquarters would be built on a 33-acres site near the Rhode Island Avenue Metro subway station. The building itself would occupy 24 acres of the tract, situated beside Brentwood Road NE between New York and Rhode Island avenues. Plans for a new GPO headquarters have been debated for more than a decade.

The president's endorsement and a similar move yesterday by a key House committee were widely viewed as signaling a breakthrough that could lead to congressional approval of the proposed building in the coming months.

The House Public Works and Transportation Committee adopted a resolution yesterday asking for government recommendations on the GPO project.General Services Administration officials said yesterday that a formal proposal would be submitted to the committee within two weeks.

Carter's action yesterday cleared the way foraccelerated congressional authorization of a new GPO building. In a letter to the committee chairman, Rep. Harold T. Johnson (D-Calif.), the president said he had "concluded that the new facility is indeed warranted" and he designated it as what is termed a "public" rather than "special purpose" building. This designation permits the House and Senate public works committees alone to authorize the construction, without further consideration on the House or Senate floor.

A White House spokesman said Carter's support for the proposed GPO building primarily represented a willingness to accede to congressional desires. Funds for the project must be included in Congress's own budget. "He's not standing in the way of what they (in Congress) want to do," the spokesman said.

Yesterday's actions were immediately welcomed by District of Columbia officials, who have long sought to keep GPO from moving its headquarters outside the city.

J. Kirkwood White, an assistant city planning director, said yesterday that the current GPO plan would retain thousands of jobs in the city, encourage increased use of the Metro subway system and possibly provide "a stimulus" to development in the New York Avenue corridor.

GPO, the government's main publishing house, produces the Congressional Record, passports, postcards and about 27,000 other publications, ranging from transcripts of former president Richard M. Nixon's tape recordings to the Warren Commission report on President John F. Kennedy's assassination.

The government's annual printing expenses are about $500 million. GPO itself does about 30 percent of the government's printing, while purchasing the remainder from private printing companies.

GPO currently operates in facilities that have long been described as outmoded. The agency is housed in seven principal buildings that are scattered about the Washington area, including its eight-story headquarters at North Capitol and H Streets near Union Station. The proposed Northeast Washington headquarters is intended to repplace all seven present GPO buildings.

One of the key features of the proposed new GPO buuilding is a plan to "horizontalize" its printing operations by spreading them across a huge, single-story structure. "What we have now is very inefficient and costly," GPO spokesman David H. Brown said yesterday. We're always moving materials from one floor to another."

Officials say the proposed GPO plant would cut the agency's costs by $15 million to $16 million annually - in effect, they said, recouping the government's outlay for building and equipping the new GPO headquarters in slightly more than 10 years.

GPO now has about 7,600 employes, but it has been gradually reducing its work force by modernizing its printing equipment. Officials say the new GPO headquarters would house about 6,300 employes, working on three around-the-clock shifts.

It would have 900 parking spaces for employes and 50 for guests. Many workers are expected to commute by subway. GSA officials, who have already drawn up tentative plans for the building, say it could be completed in five years.

Controversy has surrounded efforts to find a new location for GPO since the early 1960s. Sites that have been debated and eventually rejected have included the Bolling-Anacostia airbases, the District's reformatory complex in Lorton, Va., the Fort Lincoln "new town" area of Northeast Washington, and a tract near the Capital Beltway in Prince George's County.

Though cost estimates likely will be revised, GSA officials said yesterday that the cost of the proposed GPO building certainly would exceed the $129.1 million spent for the J. Edgar Hoover FBI Building on Pennsylvania Avenue, the most expensive government building to date.