Djokovic's comment, which he wrote on the camera lens after his first-round win over Aleksandr Kovacevic on Monday, received criticism from the Kosovan tennis federation, while France sports minister Amelie Oudea-Castera said his sentiments were "not appropriate" and "shouldn't happen again."
Despite the criticism, Djokovic said the comment is "something that I stand for" following his 7-6 (2), 6-0, 6-3 victory against Fucsovics.
"I would say it again, but I don't need to because you have my quotes if you want to reflect on that," Djokovic said. "Of course I'm aware that a lot of people would disagree, but it is what it is. It's something that I stand for. So that's all.
"You know, drama-free Grand Slam, I don't think it can happen for me. You know, I guess that drives me, as well."
Djokovic said he had "no more comment" and that he had said what he needed to say when asked if he had any response to Oudea-Castera.
Djokovic's comments came amid political tensions in Kosovo. Thirty NATO peacekeeping soldiers were injured Monday in clashes with Serb protesters in the northern Kosovo town of Zvecan, where Djokovic's father grew up.
Many Serbs, who comprise a majority in Kosovo's north, have never accepted the country's 2008 declaration of independence from Serbia. They still see Belgrade as their capital more than two decades after a Kosovo Albanian uprising against Serbian rule. Ethnic Albanians make up more than 90% of the population of Kosovo as a whole.
Monday's clashes came as ethnic Albanian mayors took office in Serb-majority areas following elections that the Serbs had boycotted.
"Kosovo is the heart of Serbia. Stop the violence," Djokovic, a 22-time Grand Slam champion, wrote in Serbian on a TV camera at Roland Garros.
Djokovic later explained that he was against war, but he defended his statement and described Kosovo's situation as a "precedent."
"As a son of a man born in Kosovo, I feel the need to give my support to our people and to entire Serbia," Djokovic told reporters. "My stance is clear: I am against wars, violence and any kind of conflict, as I've always stated publicly. I empathize with all people, but the situation with Kosovo is a precedent in international law."
Kosovo tennis federation president Jeton Hadergjonaj said in a statement that Djokovic's comments after Monday's match and on Instagram "are regrettable."
Hadergjonaj accused Djokovic of using his status as a well-known personality to stir tensions.
"Novak Djokovic was already the author of similar actions in the past. Despite a general message against violence, the statement 'Kosovo is the heart of Serbia' and further statements after the match, made by such a public figure, on the occasion of a worldwide event like the French Open, directly result in raising the level of tension between the two states, Serbia and Kosovo," Hadergjonaj's statement said.
French sports minister Amelie Oudea-Castera said Wednesday that Djokovic's message was "not appropriate" and warned that he should not do it again.
Speaking on TV station France 2, Oudea-Castera said French Open director Amelie Mauresmo spoke with Djokovic and his entourage to insist on the principle of "neutrality" on the field of play.
"When it comes to defending human rights and bringing people together around universal values, a sportsperson is free to do so," she said, but added that Djokovic's message was "militant, very political" and "must not be repeated."
The International Tennis Federation has not opened a disciplinary case.
"We received a letter from Kosovo, which we have answered," ITF president David Haggerty said. "But essentially we have forwarded their letter to the French federation, to the French Open, it's their tournament, and to the ATP who have the rules -- the two of them together have the rules and regulations for the event."
On Tuesday, the French Tennis Federation, which organizes the French Open, said in a statement: "The same rules apply to all four Grand Slams. The tournament referee and Grand Slam Supervisors ensure that these rules are complied with.
"Messages are passed on to the teams of any players concerned by such matters."
Reuters and The Associated Press contributed to this report.