WASHINGTON, Sept. 14— Guided only by radio signals from four satellites 11,000 miles in space, a civilian aircraft today followed the contours of the Potomac River for 12 miles and then returned down river to a perfect landing at National Airport.

Federal officials hailed the demonstration as a milestone in the history of aviation. The new system of navigating by satellite signal will be cheaper, more precise and more flexible than the present system of land-based radio signals, they said.

In the demonstration the pilots did not touch the controls as signals from the satellites were used by the plane's automatic pilot system to follow the river. But, the pilots did handle the takeoff and landing, when the plane had to follow directions from air traffic controllers to avoid other aircraft.

The new system, which is already being used by the military and for marine navigation and mapping, is expected to be a special boon for commercial airliners crossing oceans, where land-based navigational aids are rare. It is also expected to prevent a recurrence of an airliner's flying over hostile territory, as Korean Air Lines Flight 007 did on Sept. 1 1983, when it was shot down by Soviet fighters, killing 269 people.

In addition, the system is expected to be a great benefit at 2,500 secondary American airports that lack sophisticated ground-based systems and are forced to close when weather conditions limit visibility. A Major Advance

The officials said the system, which would cost the Government about $400 million annually, would begin operations with civilian aircraft late this winter and would be in routine use by mid-1995. The annual cost will cover satellite maintenance and installation of ground transmitters at airports.

"This is probably one of the most important advances in the history of aviation navigation," said David Hinson, the head of the Federal Aviation Administration, who joined reporters and television camera crews on the first demonstration flight on a civilian aircraft.

"In time, we hope to be capable of takeoffs and landings in zero visibility," Mr. Hinson added.

Because of the satellite navigation system, the Government will no longer need to replace aging radar units, or buy, install and maintain electronic beacon systems at airports, F.A.A. officials said.

Initially, the new system will supplement the land-based navigation system, which it will gradually replace. Air traffic controllers will still be needed to direct flights, but they will benefit by receiving more accurate position reports from pilots. If the new system is disrupted for any reason, a backup radio network will alert pilots.

The system is expected to save the airlines money by letting more planes use favorable routes, thereby reducing flight time and fuel costs and allowing greater use of the aircraft.

Before taking off this morning in a slight haze, the 14-seat Gulfstream IV taxied past a newly installed $100,000 transmitter that will replace $1 million electronic beacons that are now required at the beginning and end of every runway at major airports.

The aircraft's satellite-signal receiver system, manufactured by Honeywell Inc., costs $15,000 and does not require extensive training for pilots. That is a relatively small expense when contrasted with some airlines' estimates that the move to equip jetliners with a telephone and fax system costs about $650,000 a plane. For a major airline, equipping all planes with transmitters would cost about $7 million, but it is anticipated that the expense would be quickly recovered.

On today's flight, an airport transmitter atop a hangar at National Airport here allowed the aircraft's receiver to fine-tune the radio signals sent from space and reconcile any slight discrepancies. The system is based on 24 satellites, each sending continuous signals. Readout for Pilot

By measuring the travel time of signals transmitted from four satellites, a receiver can calculate its distance from those satellites and determine its latitude, longitude, altitude and time. The receiver then gives the pilot exact readings of those four coordinates on the instrument panel.

Each satellite actually sends out two signals, one encoded for the military, the other for nonmilitary uses. The military signal is slightly more accurate than the nonmilitary, but the extent of the difference is classified, said an aviation administration spokesman, Robert Buckhorn.

The Gulfstream IV made two round trips up the Potomac and back. The only time the pilot's hands were on the controls was during takeoff and from the time the aircraft was about 30 seconds from touching down.

The F.A.A. intends to make the new system available to civilian aviation throughout the world, without user fees. "This offers the entire world the opportunity to have concise, precise navigation," Mr. Hinson said. Developed for Military

The navigation system was developed by the Department of Defense at a cost of $10 billion, and was extensively used during the war in the Persian Gulf. The first navigation satellites were launched by a Delta rocket in 1989.

The system has attracted the interest of makers and operators of ships, trains and cars, as well as surveyors, geologists and other scientists and map makers who require precise time and geographic measurements.

"The Global Positioning System is a classic example of technology transfer from one Government agency to another," Mr. Hinson said. "Surveyors are using G.P.S. today to pinpoint locations within centimeters. Mariners are placing buoys with precision, navigating their way across oceans, and sailing their recreational boats unerringly across lakes and rivers. Surface vehicles are being traced and dispatched through busy cities."

Diagram: "The Global Positioning System" With 24 satellites orbiting 11,000 miles above the Earth, the Global Positioning System would allow pilots to navigate in all weather conditions anywhere on Earth. Only four satellites would be used at one time to navigate a plane. 1. Satellites orbiting 11,000 miles above the Earth emit signals to a receiver on a plane. 2. The airplane's receiver calculates its distance from each satellite, and uses the satellites' positions as precise reference points to determine the plane's latitude, longitude, altitude and time. 3. A ground receiver at a known location calculates and corrects for any errors in measurements. 4. GPS, as the system is known, is intended to allow aircraft to make curved approaches to airports and fly more efficient routes. The sustem is already in use for marine navigation and mapping.