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Yes, Iraq has both a President and a Prime Minister.
Nuri Al-Maliki is the Prime Minister for Iraq.
Salih Al-Mutlaq is the Deputy Prime Minister for Services for Iraq.
I found out Nouri al-Maliki is the Prime minister of Iraq in 2010 but i and no sure when he became a prime minister
Rowsch Nuri Shaways is the Deputy Prime Minister for Economic Affairs for Iraq.