President Reagan called yesterday for getting the government out of the railroad business by cutting federal spending on trains by $5.3 billion over the next five years.

The administration proposed ending all aid to Conrail and rural freight lines, slashing subsidies to Amtrak and curtailing reconstruction of the Washington-to-Boston rail route.

The proposals would require Amtrak to double fares on some passenger trains or close them down and would lead to abandonment of thousands of miles of rail lines.

Three-quarters of the federal expenditure on railroads would be eliminated, reducing the government's rail bill from this year's $1.4 billion to $356 million a year by 1986.

None of the administration's plans could be put into effect without the approval of Congress, which repeatedly has voted federal aid to help build and operate railroads.

"Congress would definitely have a lot to say about any budget changes affecting our system," said a spokesman for Amtrak. Conrail and congressional rail supporters withheld comment on the administration's proposals, which were released to the press but were not given to the affected agencies or Congress.

Conrail, the government-chartered corporation that runs freight and commuter trains in the northeastern United States, would lose all federal funding after next year under the administration's proposal. Since it was created by Congress in 1976, Conrail has cost the taxpayers $5.7 billion, almost three times the $2.1 billion originally estimated.

Conrail is expected to report a loss of $243 million for 1980, and the Reagan administration estimated that maintaining the status quo will require another $1.5 billion to $2 billion in the next five years. The administration said it is willing to give Conrail another $435 million this year and $150 million the year after that before it cuts off federal funds entirely.

The administration said Conrail could get along without federal aid if it abandoned some of its lines, cut its work force and turned to state and local governments for support.

Along with cutting off Conrail, the administration advocated an immediate end to the Local Rail Service Assistance program, which provides subsidies to little-used freight lines, primarily in rural areas. No new money would be provided for the program, which would dwindle away as work now in progress is completed.

"Traffic on these lines is so light that interstate commerce will not be disrupted," and "the government has little interest in the retention of marginal rail lines," the budget cutters said.

The biggest share of the money that Reagan wants to save would come out of the budget of Amtrak, the government-operated national passenger train system. The administration called for cutting Amtrak's subsidy in stages by raising fares to cover more and more of the cost of running the trains.

Amtrak fares now cover only about 40 percent of operating costs. Reagan's policy calls for boosting fares enough to pay 50 percent of ther operating costs by 1982, then 60 percent by 1983, some 70 percent by 1984 and 80 percent by 1985.

Maintaining the present Amtrak system will cost $900 billion this year, and the Amtrak bill will escalate to $1.4 million by 1986 unless something is done, the administration estimated. Reagan's proposal would cut Amtrak subsidies by $431 million next year, and the savings would increase to $1.1 billion in 1986.

The administration estimated that fares "will approximately double on short-distance trains, increase approximately 50 percent on long-haul trains and rise slightly on Northeast Corridor routes," which are heavily used and come closer to self-sufficiency than other routes.

"It is not fair for the general taxpayer to subsidize that portion of the population which rides Amtrak trains," the administration said.

The administration also urged cutting $300 million from the $2.5 billion now being spent to upgrade the rail line between Washington and Boston.

That project "places needless emphasis on improving trip time," the administration concluded.