In 2013, the club qualified for its first ever continental tournament, the Copa Sudamericana, through their placement in the aggregate table (Apertura & Clausura combined).

In 2017, the club finished sixth in the aggregate league table, meaning it qualified for the 2018 Copa Sudamericana, their second time participating in the competition.

Then they faced Colombian side Millonarios F.C., where they drew the first leg 1-1 at Estadio Defensores del Chaco in Asunción.

General Díaz lost the second leg 4-0 at Estadio El Campín in Bogotá, and were knocked out of the tournament with an aggregate score of 1-5.

[4] Note: Flags indicate national team as defined under FIFA eligibility rules; some limited exceptions apply.