Federal Aviation Administrator Donald D. Engen, citing improvements in scheduling practices and air traffic control, told the airlines yesterday that on April 1 he will remove minute-by-minute restrictions on the number of flights at airports in Atlanta, Chicago, Denver and the New York City area.

The decision to forgo restrictions, in place since last November, "does not mean that delays will no longer occur," Engen said in a letter to the Air Transport Association, but that "as a result of actions taken by the agency and the users, the amount of delays experienced should be reduced and will be more manageable."

Less-stringent, 19-year-old restrictions on total flights per hour at Washington National Airport, Chicago's O'Hare and New York's LaGuardia and Kennedy airports will continue, although those too are under review, Engen said.

Thus, after April 1, "Carriers are free to make any scheduling additions or adjustments they wish to make at Atlanta, Newark and Denver." They will be somewhat freer to schedule additional flights at Chicago, Washington and the New York airports, but those cities will continue to be subject to the older rules, he said.

Before the restrictions, "the air traffic system was experiencing an unprecedented amount of delays," Engen said. Last August, daily delays of 15 minutes or longer averaged 1,400 nationwide, and the number climbed to 1,600 by October.

Between Nov. 1 and Jan. 31, he said, "the average daily delays equaled 863, a reduction of 46 percent from the October numbers." Not all delays are attributable to airport congestion or air traffic control problems; over the years the FAA has blamed about 60 percent of them on weather.

Engen's letter comes after top FAA officials met individually with a number of airline executives to discuss the needs of competitive carriers and explain the realities of both the air traffic control system and the availability of runway space at the cities affected.

The system still is recovering from the effects of President Reagan's firing of 11,400 air traffic controllers, who struck illegally in August 1981 and were replaced. At the same time, a strong economy and airline deregulation have put added pressure on the system, which is carrying more passengers now than before the strike.

A concurrent development, and one that Engen clearly is hoping will avert delays like those last summer, is the increasing ability of the FAA to monitor traffic nationwide through its computer system and to redirect planes to less-busy routes. Further, more of his newly hired controllers are reaching full proficiency, which also improves traffic flow. The result is more even spacing of arrivals and departures at major airports and fewer delays.

The airlines, Engen said, have continued to operate the schedules they adopted when the restrictions were put in place and "will not revert to the bunching of large numbers of operations within small time frames."