One letter sent to the Qantas chief, Irishman Alan Joyce, used racist language and said "The unions will fight you..Qantas is our airline, started & staffed by Australians, not foreign filth like you..."
Joyce said police were investigating the threats and that he had issued a memo to 35,000 Qantas staff alerting them to the threats and attacks.
"I think it is vile. I think it's cowardly. Intimidation and bullying in any workplace...is something we should not allow," Joyce said.
Qantas has been hit by a series of strikes triggered by a dispute over pay and conditions and plans to cut domestic job cuts as the airline expands in Asia.
Joyce's memo told Qantas staff that if they felt threatened to call for help and warned that anyone involved in bullying and intimidation would "face the full consequences".
He also called on union leaders to "desist from inflammatory language and to encourage their members to exercise restraint". He said on Wednesday he did not believe that union leaders were responsible for the threats.
"There's no place for violence in any industrial campaign. There's no room for acts of intimidation and violence," said Transport Workers Union official Wayne Forno.
The Australian Licensed Aircraft Engineers Association said it had already called on its members to obey the law.
"We sent a message again about a month ago to our members, 'Just play it legally' because that's what worked last time," said the union's national secretary Steve Purvinas.
