"I will not sign a document recognizing any gender other than male and female, or gender fluidity, when a person says they feel male or female at different times," Vucic said on air of Serbian TV.
He also said that Serbian Prime Minister Ana Brnabic supported such ideas, including legalization of marriages for same-sex couples.
"As long as I am president, this [legalization of non-binary genders and marriages for same-sex couples] will remain prohibited," Vucic said, adding that Serbian society is traditional.
Serbia has been criticized by the European Union for its conservative position, Vucic said, and suggested that he was to blame for that.
In earlier comments on the matter, Brnabic, Serbia's first female and openly gay prime minister, said that she would never share the view that the LGBT community was against the "traditions and values" of Serbian society.