Horton described Sun as a "drug cheat" last week and refused to retract the comments after defeating his rival in the 400m freestyle final at the Rio 2016 Games on Saturday, reports Xinhua.
"We have been noticing what has been said in the past two days by Horton, who launched a malicious personal attack (on Chinese swimmers)," Chinese swim team manager Xu Qi said on Sunday.
"We think his inappropriate words greatly hurt the feelings between Chinese and Australian swimmers. It is proof of a lack of good manners and upbringing. We strongly demand an apology from this swimmer."
Sun, who won gold in the 400m freestyle and 1500m freestyle at the London 2012 Olympics, served a three-month ban in 2014 after testing positive to a banned substance.
The 24-year-old said he unwittingly took the drug as part of treatment for a chronic heart problem.
After winning the gold medal race on Saturday, Horton said: "I used the words drug cheat because he tested positive. He's one of the athletes here who has tested positive."
The Australian's comments prompted a heated response on social media, where many Chinese fans describing the remarks as unjustified.
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