Barely 24 hours after President Reagan called for massive cuts in federal railroad subsidies, Amtrak yesterday sent Congress a request for $250 million more in government aid than the president wants to give it.

Even so, Amtrak President Alan S. Boyd said Amtrak plans to cut service in the Washington-to-Boston corridor by three trains a day, cancel The Shenandoah from Washington to Cincinnatti and The Cardinal from Washington to Cincinnati to Chicago, and cut short the route of a Chicago-to-Texas train called the InterAmerican.

Boyd said the trains will be dropped Oct. 1 because traffic on them does not meet the minimum standards set by Congress for continued operation.

To run the rest of its nationwide rail network, the government passenger rail system asked for $176 million in federal operating subsidies for fiscal 1982 and another $254 for equipment and captial improvements.

The $970 million request contrasts with a total Amtrak appropriation of $613 million recommened Wednesday in the Reagan administration's budget message, which called for cutting rail subsidies by more than $5 billion in the next five years.

The administration said Amtrak's budget should be cut because only 1 percent of the people ride Amtrak and "it is not fair for the general taxpayer to subsidize that portion of the population which rides Amtrak trains."

As for the $613 million Reagan request, "We have not made any calculation on that basis, and we do not intend to," Boyd said at a press conference.

Congress has told Amtrak what kind of a passenger train system it wants, and "we're going to tell Congress that if the system operates as we outlined, this is what it will cost," he said.

"There's a saying in this town that the president proposes and Congress disposes," added Boyd, who also said he is confident that Congress will continue to vote funds to upgrade rail lines in the Northeast Corridor between Washington and Boston, another target of Reagan administration budget cuts.

The corridor improvement project, under way for several years, is meant to cut the train travel time between New York and Washington from the present four hours to two hours and 40 minutes.

That project "places needless emphasis on improving trip time," a Reagan administration budget proposal said.

The administration said Amtrak should raise its fares to cover 50 percent of its operating costs next year, 60 percent in 1983, 70 percent in 1984 and 80 percent in 1985.

Boyd said Amtrak is aiming to cover 50 percent of operating costs by 1985 and expects to meet that goal. The passenger train system might might meet the Reagan goals if it operated on the same basis as other modes of transportation, he said.

Amtrak builds all its own stations, while airports are built by local governments, and Amtrak pays for its own tracks, but bus and truck lines don't have to finance their own roads, he noted.