The violence erupted after ethnic Albanian mayors took office in northern Kosovo's Serb-majority area following elections that were boycotted by the Serbs.
"Novak Djokovic has yet again promoted the Serbian nationalists' propaganda and used the sport platform to do so," Ismet Krasniqi, president of Kosovo's Olympic Committee (KOK), said in a statement.
France's Sports Minister Amelie Oudea-Castera, whose country will host the summer Olympics in Paris next year, said Djokovic's message was "not appropriate, clearly".
Djokovic, chasing a record 23rd Grand Slam title, has said he was not holding back and would do it again.
On Tuesday, Kosovo's tennis federation said Djokovic's comments were "regrettable", accusing him of using his status as a well-known personality to stir tensions.
Persons:
Roland Garros, Serbia's Novak Djokovic, Aleksandar Kovacevic, Novak Djokovic, Djokovic, Ismet Krasniqi, Amelie Oudea, shouldn't, Hungary's Marton Fucsovics, Rohith Nair, Karolos Grohmann, Julien Pretot, Shrivathsa Sridhar, Helen Popper, Christian
Organizations:
U.S, REUTERS, Kosovo Olympic, International Olympic Committee, NATO, Serbs, Kosovo's Olympic, IOC, Thomson
Locations:
Paris, France, PARIS, Serbian, Kosovo, Serbia, Zvecan, Kosovo's, Bengaluru, Karolos