Appointed last December, Pinter managed the national eleven in five matches, with a record of two victories, a draw and two defeats.
On September 7 Hungary suffered a shocking 2:1 defeat from Northern Ireland in a European qualifier on home ground.
Dardai, who had been capped 61 times, is now employed by Hertha BSC.
The three qualifiers will be played in Romania on October 11, on Feroer Islands three days later, and against Finland on home ground on November 14