The Department of Transportation yesterday recommended a sharp cut-back in the Amtrak railroad passenger system to prevent Amtrak's deficit from soaring to $1 billion by 1984.

The reduced system advocated by DOT would serve the nation's 36 largest cities and 160 metropolitan areas, but would raise to eight the number of states without passenger service.

DOT said the new network would serve 90 percent of Amtrak's passengers with two-thirds of its track.

The changes would not affect routes in the Northeast Corridor, core of the Amtrak system.

Calling the decision to cut passenger service "a political hot potato," DOT Secretary Brock Adams said, "I'm trying very hard to avoid third-degree burns from it."

Unless the Amtrak system is pruned from the present 27,000 miles to about 18,900 miles, the government subsidies needed to keep the trains running will reach $1 billion by 1984, Adams said.

Even the curtailed rail network will require $800 million in subsidies by that date. The fiscal 1977 deficit was $529 million.

Forecasting the need for permanent federal subsidies for Amtrak, Adams said the government may have to take a greater role in running the system. Amtrak now is governed by a 13-member board with nine government representatives but is not directly responsible to Dot.

The earliest any of the trains might be dropped is July 1979, Adams said. Public hearings first must be held, and Congress will have the chance to veto any DOT decisions over Amtrak routes.

The truncated system recommended yesterday "is going to be very tough to sell to congressmen who are concerned about passenger service out in the districts," said one Capitol Hill aide who works closely on Amtrak apporpriations.

Among the trains Adams recommended dropping is the Shenandoah, from Washington to Cincinnati, which serves the district of Rep. Harley Staggers (D.W. Va.), chairman of the House Commerce Committee.

Also marked for extinction are trains backed by members of Congress from Louisiana, Florida, Arkansas and Tennessee who helped Amtrak get an $18 million suppelmental appropriation this year.

"Congress would like to keep the trains running, but it doesn't like to spend the money," Adams said at a press conference. He warned that if Congress forces Amtrak to keep unprofitable routes, "There is the danger of the whole system going down."

Adams also indicated Amtrak might have to increase its fares so the federal government does not pay for all of its cost increases, which he acknowledged are rising faster than those of other railroads.

Amtrak passenger revenues covered almost 50 percent of the operating costs in 1971, but last year paid only 37.4 percent. Meanwhile, the federal subsidies have risen from 5.3 cents per passenger mile to 12.7 cents.

DOT officials said they do not know how many cities wouls lose passenger service under the plan, because final routes for several sections of the country have not been determined.

Among the trains that DOT recommended be dropped are The Floridian, between Chicago and Florida; the Inter-American, between Chicago and Mexico; and the San Francisco Zephyr, from Chicago to the West Coast.

Also to be dropped are the Pioneer from Salt Lake City to Seattle, and the Empire Builder and North Coast Limited, which run on parallel routes from Minneapolis to Seattle and will be replaced by a single train.

The National Association of Railrod Passengers critcized the DOT recommendations, saying the Amtrak system should be expanded rather than contracted, and warning that service cuts will lead to loss of ridership and rising costs.

In addition to Maine, New Hampshire and South Dakota, which have never had Amtrak service, Arkansas, Nebraska, Wyoming, Utah and Nevada would be left out of the national rail passenger network.