Both sides said they would have no public comments -- at least until the negotiations are set to finish on Thursday.
It was not immediately clear if the blackout was imposed by the federal mediator or was a deal struck between the company and union.
The meeting is the first since May, when union leaders said they were close to a deal, but that the airline's offer just wasn't enough. It also is the first with a new mediator.
American's last offer included a 3 percent signing bonus and a 9.9 percent pay raise over five years. Differences remained over health care, work schedules and other benefits.
Going into the meeting, both sides indicated Tuesday would be largely be a "getting acquainted" session before getting down to business Wednesday and Thursday.
The Association of Professional Flight Attendants represents nearly 18,000 American employees.