The Federal Aviation Administration said yesterday that during the first three months of this year there were 20 near collisions in the air in which a commercial airliner came within 500 feet of another airplane -- an increase of nine over the same period a year ago.

FAA Administrator Donald D. Engen said his agency released the preliminary statistics "so all concerned will exercise increased judgment during the spring and summer, when historically such incidents occur with more frequency."

Engen said he had expected the increase because of improved reporting systems within the FAA and increased emphasis on pilot reporting.

However, the statistics come as the number of flights is increasing and when the FAA's air traffic control system is under pressure to handle more airplanes.

In most of the incidents, Engen said, at least one of the aircraft involved was neither in contact with nor under the direction of air traffic controllers.

Many private and military flights operate on their own; all commercial flights are required to maintain communication with air traffic controllers.

There were 141 near collisions in the air reported during the first quarter, involving all categories of airplanes; a year earlier there were 98.

In the more critical category -- those in which airplanes come within 500 feet of each other -- there were 108 incidents during the first quarter, compared with 53 a year earlier. In other words, there was more than a doubling of more-critical incidents reported.

In only one of the 500-feet-or-closer incidents were both planes commercial flights. There were 15 incidents involving commercial planes and private planes, and four involving commercial planes and military flights.

In 44 of the 108 incidents, both planes involved were private aircraft; 31 of the incidents involved private and military aircraft, and in 10 incidents both planes involved were military. In three instances, both aircraft could not be identified.

During the same period there was only one midair collision, involving two private planes. Two persons were killed.

Also yesterday, the National Transportation Safety Board urged the FAA to improve coordination between controllers after a mixup that nearly caused two jumbo jets to collide on a Minneapolis runway March 31.

One controller radioed one of the jets to cross the runway at about the same time that another controller gave the other jet permission to take off on the same runway.

"It is already evident," the board said, "that deficiencies in coordination" were involved.