A consumer group asked the Interstate Commerce Commission yesterday to order Southern Railway Co. to continue running the Southern Crescent from Washington to New Orleans until Amtrak can take it over.

The Crescent is the last privately run, major intercity passenger train in the East. Southern wants to stop service after Aug. 6 because its losses on the train last year amounted to $6.6 million.

The Department of Transportation has proposed that Amtrak, the government-run rail passenger agency, take over the Crescent's route. But that would not take effect before May 1 1979 at the earliest after Congress has passed enabling legislation. Amtrak and Southern both think the change-over date would be much later.

The National Association of Railroad Passengers, representing U.S. consumers, seeks to avoid any interruption in service. NARPs Executive Director Ross Capon told the ICC yesterday: "It would be senseless to allow the possibility of discontinuance of the train this summer, which would then make the likely restoration of the service at a later date more difficult and costly."

He explained that riders would accustom themselves to other transportation and Southern might divert its personnel and train station to other uses.

Southern had originally asked to halt service last month, but the ICC pushed back the date to August. The delay could cost the company stands to lose $2.2 million on the Crescent. Were Southerns to run the train until April 1979, its total loss would be $6.7 million. Another year's delay, which might be necessary if capital improvements have to be made by Amtrak, could cost Southern another $6.7 million.

Last week a Southern executive testified that ridership on the Crescent would have to be increased 121 percent just to break even. Capon accused Southern yesterday of failing to promote the train sufficiently through advertsising and off-peak fares. He also said Southern had failed to develop mail traffic, while most Amtrak long-distance trains now carry mail.