American rail passengers were served a double dose of tough medicine last night:

The imminent death of the nation's one remaining major intercity train under private ownership, the Washington-Atlanta-New Orleans Southern Crescent, was announced by Southern Railway.

A 2 1/2 percent average fare increase for most other passenger trains was announced by Amtrak, effective April 30.

Washington-based Southern's plans to drop the Southern Crescent effective April 6, came after several months of negotiations with Amtrak on a takeover of the train failed.

According to Southern President L. Stanley Crane, the rail firm offered all passenger equipment -- 17 locomotives and 81 passenger cars valued by the company at $4 million -- to Amtrak, a federally subsidized corporation set up by Congress at the start of this decade to operate intercity trains.

In addition, southern offered to provide not more than $2.7 million to Amtrak to underwrite the train's losses through Oct. 1. Crane said that if Amtrak did not agree that the $4 million figure was "fair and reasonable," the company would offer that amount in cash.

At a board meeting on Wednesday, Amtrak's directors rejected the Southern plan. Crane said his firm would file a petition with the Interstate Commerce Commission on Monday, seeking to abandon the service.

Southern has been losing $500,000 a month on the Crescent, which operates between Union Station and Atlanta daily. Three times a week, the train operates between Atlanta and New Orleans. Southern's train connects here and in New Orleans with amtrak service, providing through connections from Boston to Los Angeles.

Crane said his company will keep its offer to Amtrak open until April 5. The firm's willingness to substitute cash for the equipment is being studied by Amtrack's management, which could make a substitute proposal to Amtrak directors at a future meeting.

The Southern decision comes at a crucial time for Amtrack, which faces the prospect of sharp curtailments in service across the country without new subsidies from the federal government.

The Department of Transportation currently is studying Amtrak's routes. It will make recommendations on what trains can be dropped or consilidated with others by May 1.

Crane said the decision to stop Southern's final passenger train --called the "Cadillac" of rail service by a DuPont Co. official recently -- came "only with the greatest reluctance."

He noted that his firm has decided not to join most other firms in the industry, which turned their passenger operations over to Amtrak in 1971. Since then, Southern has lost $30 million on passenger service, although its highly regarded trains have represented a public relations gain, company officials have stated.

The ICC can order Southern to continue operation of the train while it holds hearings on the proposed discontinuance. Thus, although the rail firm wants to stop the train or transfer it to Amtrak by early April, ICC proceedings could keep the train alive through the summer.

In the fare decision announced yesterday, Amtrak said new rates will include higher prices during periods of peak travel on key routes. The 2 1/2 percent overall increase goes into effect April 30, and the peak period charges will be effective from June 15 through Sept. 5.

Amtrak's last fare increase, also 2 1/2 percent, took effect Oct. 30.

among trains for which amtrak will introduce special peak-period charges are the Washington-Montreal Montrealer, the Washington-Chicago Broadway Limited, and New York-Miami trains, which stop in Washington.

Peak-period rates for single sleeping accommodations will be boosted by up to $20 on East Coast trains and $20 on western trains.