"The conduct of a small number of Australian soldiers had brought the armed forces into disrepute," Smith said. He said he had contacted Afghan Foreign Minister Abdul Rahim Wardak over the offensive posts.
"I apologised to him on behalf of Australia," Smith was quoted as saying by the Australian Broadcast Corporation radio.
The soldiers were caught out describing Australian Prime Minister Julia Gillard as a "f***ing ranga", and Afghans as "sand c**ns", "dune c**ns", "n*****s" and "smelly locals".
"I made the point to him that the chief of the defence force and the chief of army were investigating this matter and in all likelihood disciplinary proceedings would follow," he said.
The defence minister said Wardak responded by saying that he did not believe the incident would diminish the standing of Australian troops in Afghanistan. Soldiers found to have taken part in the offensive behaviour could be sent home.
A video posted on Facebook, broadcast by Channel Seven, features a local man shown running away from an explosion, with an Australian soldier heard to say that the blast "scared the f*** out of that mufti". Another Afghan is referred to as a "raghead". He warned those found responsible would be sent back to Australia."In advance of that investigation, it is open to a local commander if he believes that, prima facie, conduct has occurred which would warrant action, he can take it on the ground," Smith said.