Kursky District () is an administrative district (raion), one of the twenty-six in Stavropol Krai, Russia. Municipally, it is incorporated as Kursky Municipal District. It is located in the southeast of the krai. The area of the district is . Its administrative center is the rural locality (a stanitsa) of Kurskaya. Population: 52,100 (2002 Census); 43,303 (1989 Census). The population of Kurskaya accounts for 22.3% of the district's total population.