 He joined the diplomatic service of Serbia in 1891, as the secretary of the Serbian Legation at Constantinople.In 1893, Vesnić was appointed as a university professor teaching international law at Grande École in Belgrade and the same year became MP in the National Assembly of Serbia as a member of the People's Radical Party of Nikola Pašić.In the government of Sava Grujić (1893–1894), Vesnić was the Minister of Education and Religious Affairs.