ATLANTA (AP) _ Air traffic controllers opened their first convention today since their new union was certified, and leaders pledged not to use a strike threat as a bargaining tool.

''We're not out to tear down the air traffic control system,'' union organizer John Thornton declared in opening remarks to nearly 300 controller delegates representing air traffic centers and towers across the country.

An illegal strike seven years ago triggered the firings of 11,400 controllers and destroyed the old union.

Many of the controllers who joined the new union, the National Air Traffic Controllers Association, were hired by the Federal Aviation Administration after the 1981 strike.

''We might disagree with the FAA, the administration or the Congress, but those grievances are left at the bargaining table. They (controllers' grievances) will never compromise the integrity of the (airway) system,'' said Thornton, who was one of those fired in 1981.

In an appearance on ABC-TV's ''Good Morning America'' shortly before the convention opened, Thornton also called on the FAA to ''stop nickel and diming'' its hiring schedule.

Much of the three-day convention is expected to focus on writing the union's first constitution. A draft constitution already includes a clause specifically prohibiting a strike, but some delegates want to make that pledge even stronger.

On the eve of the convention delegates said they hoped the gathering would focus attention on what they said was the failure of the Federal Aviation Administration to deal with controller shortages, outdated equipment and heavy traffic loads.

FAA officials have acknowledged that their efforts to rebuild the air traffic control system continue to be hampered by a shortage of fully trained controllers, especially at some of the busiest airports where large amounts of overtime are still required.

But FAA Administrator Allan McArtor suggested recently that the battle is being won with controller errors declining sharply and new computer equipment being installed at enroute control centers. Traffic flow techniques also have cut into the number of so-called ''red sectors'' of airspace where there had been concerns last summer of sudden traffic saturation, he has said.

The improvements prompted the FAA last week to disclose that it no longer would require as routine the current spacing requirements between aircraft enroute to destinations imposed after the 1981 strike. Such separation - as much as 15 miles - now may be imposed at the discretion of officials at the enroute control centers.

But the controllers gathered for the three-day National Air Traffic Controllers Association convention drew a less rosy picture.

''There is 30 percent more air traffic than in 1978 but we have fewer controllers separating traffic than we did 10 years ago,'' said John Thornton, the union's chief organizer.

Thornton said in remarks prepared for the opening of the conference that controllers continue to face ''frustration over being excluded from FAA decision making on safety issues.''

Other controllers complained about morale problems and the failure of FAA managers to work with controllers.

''Nothing's changed (since 1981),'' complained Mike Lacefield, a controller from Bakersfield, Calif.

''I would say it's gotten worse,'' added Mark Bohn, a colleague from the Bakesfield traffic control center.

''Every controller is concerned about the amount of people we have, the amount of hours they have to work, the amount of traffic they have to work and the equipment they have to work with,'' said Dennis Delaney, controller from Pensacola, Fla., and a member of the union's interim executive board.

James Baglieri, a controller from the Chicago enroute control center, the nation's busiest, said staffing and equipment problems have controllers worried. Before the strike, the Chicago center rarely handled more than 2 million aircraft a year, but in recent years 2 million has become commonplace and last year it exceeded 2.3 million aircraft, said Baglieri.

The convention is the first for the National Air Traffic Controllers Association, which won the right to represent air traffic controllers in bargaining with the FAA in an election last June.

The election surprised many senior FAA officials because of its unexpectedly high, 85 percent, turnout and 70 percent vote in favor of the union. Since then, about 4,500 controllers have been recruited as dues-paying members, about 36 percent of the 12,500 controllers who are eligible.

''The number is growing every day,'' insisted Thornton.