Klein was accused of calling Raven Klaasen a "f***ing kaffir" during the clash at a tournament in Eastbourne.
And despite issuing a public apology, the ATP handed down a $14,000 fine to Klein, saying further penalties could arise out of a full investigation.
In a statement, Klein said he deeply regretted his actions.
"I would like to clarify my position on an incident that occurred during my match against Raven Klaasen in the last round of qualifying for the AEGON International at Eastbourne on June 14," Klein said.Klaasen’s coach Stephan de Kock later accused Klein of spitting in his direction during the match, which Klein eventually won.
"During the second set, after losing a point, I audibly used a racial slur.
"It was not my intention to racially vilify my opponent or cause offence to anybody else and I am deeply embarrassed that I behaved in this manner.
"I deeply regret my serious error in judgment in using this word and I am very sorry for the offence this has caused.
"After the match I called my opponent Raven and apologised for what had happened and also apologised for any offence caused to his support team.
"This incident is now currently being investigated by the ATP and as such I have been advised not to make any further comment."
South African tennis bosses were outraged by Klein's alleged behaviour, and lodged formal complaints with the international and Australian tennis federations.
Tennis Australia said in a statement it had suspended Klein from the Australian Institute of Sport Pro Tour Program and could impose further sanctions after an investigation.