Yes, Iraq has both a President and a Prime Minister.
Sargon Lazar Sulaywah is the Minister of Environment for Iraq.
Ali Al-Shukri is the Minister of Planning for Iraq.
Nuri Al-Maliki is the Prime Minister for Iraq.
Khayrallah Hasan Babakir is the Minister of Trade for Iraq.
Majid Hamad Amin Jamil is the Minister of Health for Iraq.
Hadi Farhan Al-Amiri is the Minister of Transportation for Iraq.
Sadun Farhan Al-Dulaymi is the Minister of Culture for Iraq.
Hasan Al-Shammari is the Minister of Justice for Iraq.
Hoshyar Mahmud Zebari is the Minister of Foreign Affairs for Iraq.
Muhammad Khalaf Tamim Al-Juburi is the Minister of Education for Iraq.
Muhammad Shia Al-Sudani is the Minister of Human Rights for Iraq.