Córdoba captained Colombia to win the 2001 Copa América competition, scoring the only goal in the final. Córdoba also played for his country at the 1998 World Cup (taking shirt number 2 from Andrés Escobar who was murdered in the previous tournament) without appearing in a match, the 2003 FIFA Confederations Cup (where they finished in fourth place), and in three other editions of the Copa América (1997, 1999, and 2007).