President Cater, in a controversial move, ordered federal agencies last night to eliminate free and low-priced parking spaces for most government employes in the Washington area and throughout the United States starting next fall.

The president's directive, which was included in his energy conservation plan, would markedly increase parking fees for executive branch employes starting Oct 1. Further increases would take place in the next two years.

The higher parking rates would apply to about 75,000 Washington-area residents who now use an estimated 27,000 free and cut-rate government parking spaces in downtown Washington, Rosslyn and the Pentagon area, government officials said yesterday. The increased rates also would affect several thousand other federal workers who park in outlying suburban areas here.

Although the president's order would not apply to the more than 8,000 free congressional parking spaces on Capitol Hill, government officials said at a news briefing yesterday that the Carter administration was "encouraging" Congress to take similar steps. Previous effects to impose parking fees for congressional spaces have been rejected.

Carter's unexpected announcement, which follows years of extensive and sometimes bitter debate, drew immediate delight from some local officials. But it is certain to anger many government workers who regard cut-rate parking as a significant fringe benefit at a time of rapid inflation.

"Obviously we're pleased," said D.C. Transportation Director Douglas N. Schneider. "We've been advocating elimination of that (parking) subsidy for a long time." Most District of Columbia government employes are required to pay prevailing commercial parking rates. Mayor Marion Barry and City Council members, however, have free spaces.

The Carter administration took note of local government pressures yesterday. Citing studies of the issue by the Office of Management and Budget, an administration statement said, "OMB agreed with the Washington Metropolitan Area Council of Governments that commercial rates for federal employes would cut down traffic and pollution."

A recent antipollution plan drawn up by Washington-area officials called for a ban on free and low-priced parking in an attempt to curb air pollutants emitted by auto exhausts. The federal government urged Washington-area governments yesterday to press in addition, for elimination of free and low-cost parking for employes of private businesses here-a move already under study by local officials.

The protractedness of the debate over free and low-cost parking here was underscored in a recent General Accounting Office study that cited a 1972 OMB draft proposal to make federal parking fees mandatory. "The 1972 draft was opposed by government agencies and was never promulgated," the report by GAO, Congress' auditing arm, said.

Under the Carter administration's new plan, as outlined in what was termed an OMB "draft circular", most federal employes would be required to pay about half the prevailing parking rates in their areas starting Oct. 1. Parking fees would rise to what was described as "the full rate" in October 1981. These rates would be calculated by the General Services Administration through analyses of commercial rental values. Officials said yesterday that the GSA computations would yeild prices "very close to commercial (parking) rates."

OMB officials said commercial rates in the Washington area now range from about $20 to $70 a month. At present, they said, about half the federal government's parking spaces here are free and the others cost an average of $10 a month.

According to OMB officials, the president's directive provides for an exemption from parking fees for employes working in areas where prevailing parking rates are $10 a month or less. It also may permit special treatment for handicapped workers and others who can cite "compelling considerations," the said. The officials said high-ranking federal officials would not be exempted from parking fees for their private cars.

OMB officials said the increased parking rates would bring in $17 to $20 million in additional federal revenue from the Washington area and $35 to $40 million nationally. In the Washington area, they said, the higher parking charges would eliminate 100,000 miles of daily auto travel, save 6,000 gasoline, and increase use of mass transit.