Djokovic’s parents travelled to Australia for the first time since his first title in 2008 to offer support to their son following his deportation last year.
A number of Russia supporters gathered on the steps outside Rod Laver Arena following Djokovic’s quarter-final victory over Russian Andrey Rublev.
Waving flags and chanting “Russia, Serbia”, they were eventually tackled by security, with four people questioned by police over the flags and threatening security guards.
Australian Open organisers were criticized for not stopping the demonstration sooner, with the video showing they were allowed to remain on the steps for several minutes.
In a statement released by the tennis star’s representatives, Mr Djokovic senior said: “I am here to support my son only. I had no intention of causing such headlines or disruption.
“I was outside with Novak’s fans as I have done after all of my son’s matches to celebrate his wins and take pictures with them. I had no intention of being caught up in this.
“My family has lived through the horror of war, and we wish only for peace. So there is no disruption to tonight’s semi-final for my son or for the other player, I have chosen to watch from home.
“I wish for a great match and I will be cheering for my son, as always.”
Srdjan Djokovic made no comment about a translation on the video that claims he said “long live Russia”.
In a statement, Tennis Australia said: “After the events of Wednesday night, we acted swiftly to work with police and our security teams to have the instigators of the protest removed from the venue.
“Throughout the event we’ve spoken with players and their teams about the importance of not engaging in any activity that causes distress or disruption.
“Mr Srdjan Djokovic has issued a statement confirming that he will not attend tonight’s semi-final.
“We will continue to strive for the safety of fans at the event and reiterate our position banning flags from Belarus and Russia.
“Tennis Australia stands with the call for peace and an end to war and violent conflict in Ukraine.”