"Global attention is currently on Iraq as the new government there focuses on rebuilding the country and combating the spread of ISIL," Mr McCully said.
"New Zealand is currently considering options for a non-combat, training role, in Iraq and this visit is an opportunity to gain the Iraqi Government's perspective on how New Zealand can best assist.
"We have already committed $14.5 million in humanitarian aid to help people displaced by the fighting in Iraq and Syria and stepped up diplomatic efforts aimed at addressing the spread of extremist ideologies."
Mr McCully said any role for the New Zealand military in Iraq would be dependent on an invitation from the Iraqi Government.
Dr al-Ja'afari will meet with Mr Key, Defence Minister Gerry Brownlee and Mr McCully during his one day visit to Auckland on Friday.