Khaled al-Attiya did not give reasons for the postponement on Sunday but government sources said the powerful Shia Alliance is deadlocked on a nominee for the interior ministry post.
Shia Alliance sources said the the Supreme Council for Islamic Revolution in Iraq threatened to reject former Shia army officer Farouk al-Araji for the interior portfolio.
Al-Araji was nominated by Nuri al-Maliki, the prime minister.
A rejection could split the bloc, to which al-Maliki belongs.
Some members of the Shia Alliance said a deal could still be struck later in the day.
Intense wrangling led al-Maliki to leave the defence and interior posts empty when he unveiled his government of national unity on May 20.