Historically part of Armenia, Artsakh, or the Nagorno-Karabakh Republic, is internationally recognised as part of Azerbaijan and has been the source of two conflicts since 1990 as well as frequent skirmishes, including what is currently being described as a blockade.
Khachanov, who is Russian but has an Armenian father, has twice written messages on the camera lens after victories during the tournament calling for Artsakh to "stay strong", while Melbourne's Armenian community have brought flags of the region to the venue.
Khachanov's actions prompted the Azerbaijan Tennis Federation to write a letter of protest to the International Tennis Federation.
Calling the messages a "provocation" and a "hateful act", a statement from the ATF concluded: "The ATF condemned this act and demanded that the tennis player be punished and urged the International Tennis Federation to take harsh measures for prevention of such incidents in the future."
The ITF is yet to make any public comment about the matter but Khachanov, who was unaware of the Azerbaijan response, said he had not been told anything by officials regarding further messages.
"I have Armenian roots," Khachanov said after defeating Sebastian Korda in the quarter-finals at Melbourne Park.
"From my father's side, from my grandfather's side, even from my mom's side. I'm half Armenian. To be honest, I don't want to go deeper than that, and I just wanted to show strength and support to my people. That's it."
Khachanov reached a second consecutive grand slam semi-final after American Korda retired with a wrist injury trailing 7-6 (5) 6-3 3-0.