The head of the Federal Aviation Administration warned yesterday that a bitter scheduling squabble between American Airlines and United Airlines will cause major delays for evening travelers at Chicago's O'Hare Airport beginning Saturday, with possible repercussions for flights in and out of other cities as well.

The problem is caused by intense scheduling competition between the two airlines that will bunch too many flights into the 7-to-8:30 p.m. time slot, FAA Administrator James B. Busey said yesterday. Busey said the jams should end Oct. 1, when another change in United's Chicago schedule is set to take effect and spread flights out a bit more evenly.

"The traveling public is going to be impacted," said Busey, who promised the FAA would work to prevent the airlines from scheduling too many flights at the same time out of the nation's busiest airport.

Problems at Chicago ripple across the nation because American and United maintain major operations there. Approximately 80 percent of all flights at O'Hare in the evening hours are either United or American or their regional affiliates.

The battle between the two revolves around which carrier will get the best schedule times for the important evening rush at O'Hare. Under a March 1, 1989, agreement with the FAA, United and American agreed to a plan to avoid having flights bunch up at certain time periods. Among other things, the two agreed they would schedule no more than three arrivals every three minutes.

Dissatisfied with its competitive position, American on June 27 told the FAA it was withdrawing from the agreement, returning to the basic "slot" system under which it can operate a certain number of flights within each half-hour period. That allowed American to schedule a slightly earlier evening rush by bunching flights within the half-hour slots, effectively superimposing its rush on United's rush.

United, which remained under the March 1 agreement, received permission from the FAA to move its schedule even earlier from Oct. 1 through Jan. 15. American, which filed suit against United when it first announced the changes in August, filed suit against the FAA earlier this week in the U.S. Court of Appeals in the District.

Busey yesterday said he hoped to clear up the Chicago mess by Jan. 15. A working group will consider alternatives, which could involve tightening the slot rules to take away the leeway provided by the half-hour slots.

Meanwhile, he said, tight scheduling at O'Hare is likely to mean delays for anyone using the airport.