Is Vatican City a state or a country?

Yes. The Vatican City (a city within a city within a country) is considered a state, with its own flag and maintaining diplomatic relations as any other country would do. additional answer... The Vatican is a city state which came into being in 1929, it has an area of 110 acres with a population of about 900 making it the smallest state in the world, It consists of a walled area within the city or Rome