Delic, who on Wednesday beat Paul-Henri Mathieu in his second successive five-set match, posted a plea on his Web site urging fans to settle down.
"As we all know, Bosnians and Serbs have had some differences in the past, however this is not the place nor time to settle those differences," the naturalized American wrote.
"Novak and I are tennis players playing in one of the greatest settings in the world of tennis. I am only hoping for a fair fight that all the fans will enjoy, with the key word being 'enjoy.' That's what we are all here for, to enjoy moments like these," he wrote.
Two rival supporters were kicked out for scuffling at a bar following Tipsarevic's defeat.
Police moved in quickly to break up the fight and eject the two men as part of their zero-tolerance policy on troublemakers.
Two years ago, the Australian Open was marred by violent clashes between an estimated 150 Croatian and Serbian fans. Last year, police used capsicum spray on a group of rowdy Greek supporters.