Iraqi leaders have so far failed to agree on the makeup of the national government. Al-Ja'fari said on April 19 that stepping down was "out of the question."
Members of the UIA have been deadlocked on whether to drop al-Ja'fari as their nominee. Al-Ja'fari faces stiff opposition from Kurdish and Sunni parties, who blame him for failing to end sectarian violence.
Alliance leaders are set to meet on April 22 to discuss the formation of a new government.