The 64-year-old Argentinian led Colombia to the World Cup quarter-finals, where they were eliminated by hosts Brazil having beaten Uruguay in the last 16 following three group-stage victories.
Colombian Football Federation president Luis Bedoya Giraldo told fcf.com.co: "Jose Pekerman has requested a period of rest for personal reasons, and it is a situation that deserves our respect.
"We will hold talks with him over his continuing future with the Colombian national team in the first days of August."
Pekerman has also coached Argentina and replaced Leonel Alvarez as Colombia boss in January 2012.
- Sports & Recreation
- Jose Pekerman