"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 broadcaster TV Pink.
He also said that Serbian Prime Minister Ana Brnabic was supportive of his stance, despite being openly gay.
"As long as I am president, this [legalization of non-binary genders and same-sex marriages] 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.