Investigators studying the fatal wreck of a Metro subway train are focusing on the actions of a Metro supervisor who was at the site of the derailment, transit officials indicated yesterday.

"We have interviewed that supervisor," Metro General Manager Richard S. Page said at a meeting of the transit authority's board of directors. "Determining exactly what he did that evening will be a key element of the inquiry."

The accident, in which three passengers were killed and at least 25 others injured, has led to three investigations. Officials of the National Transportation Safety Board have already suggested that human error--possible mistakes by the supervisor, the subway operator or other Metro employes--is a central issue.

A second, specially appointed board of inquiry, including transit specialists from New York, Chicago and San Francisco, assembled here yesterday to start its work. The panel's chairman, Francis A. Gorman, general manager of the Port Authority Trans-Hudson Corp. of New York, promised an independent investigation and a written report of findings and recommendations. Metro officials are also conducting their own investigation.

The derailment, the first fatal wreck since the subway system opened in 1976, occurred on a crowded rush-hour train bound for New Carrollton on the Orange Line Wednesday afternoon. Authorities say a manually operated rail switch near the Smithsonian station, at 12th Street and Independence Avenue SW, was improperly adjusted. The misaligned switch, officials say, caused the train to start crossing over to an incorrect track.

The transit supervisor, whom Metro officials have refused to identify, was at the site to adjust the switch manually. The train stopped with its front wheels on the wrong track. According to official accounts, the supervisor then boarded the rear car, took over the controls and started to operate the train in reverse in an attempt to get it back on the correct track.

But officials say the front wheels remained on the incorrect track. With the rail car's front wheels on one track and its rear wheels on another, the car was dragged diagonally through the tunnel for a short distance and crushed against a large concrete divider, situated between the two tracks.

Answers have not yet been provided to numerous questions about these events. For example, transit specialists say that in such instances a switch must be visually inspected before the train is backed up to assure safety. Metro officials, addressing this issue publicly for the first time yesterday, gave sketchy information.

Joe H. Sheard, Metro's rail services director, said he had received reports from control room employes that the supervisor had inspected the switch before backing up the train. "It had been looked at and the switches were properly closed," Sheard said he was told. But he added, "I don't know exactly what the supervisor did." Officials did not disclose what the supervisor said about this issue when he was interviewed by investigators.

Metro General Manager Page also expressed uncertainty about whether passengers on the derailed six-car train were given adequate information and instructions as they waited for rescue. Some have complained of spending a harrowing time in nearly complete darkness.

"I'm concerned about reports that the public on this train did not get information for several minutes. I'm not sure how long that was," Page said. "I've heard reports that that was a considerable period of time. Whether that was five minutes or 30 minutes, I'm uncertain."

According to yesterday's account of the accident, crucial decisions about the train's movement were made after a series of communications among the train's operator, the supervisor at the site and control room personnel. Investigators apparently must try to establish precisely what information was exchanged in these conversations. They must also try to determine why the manually operated switch was improperly aligned.