AirTran Airways apologized Friday for an incident on New Year’s Day in which airline officials pulled nine Muslim passengers off a domestic flight and refused to rebook them, even though F.B.I. agents said they had done nothing wrong.

The incident occurred Thursday at Ronald Reagan Washington National Airport after members of a Muslim family boarding a flight to Orlando, Fla., had a conversation about the safest place to sit in the event of an accident. Other passengers reported the remarks as suspicious to a flight attendant.