Arshad Salihi, the head of the Iraqi Turkmen Front, has criticized what he described as the "under-representation" of Turkmen in the Iraqi army.
Salihi's remarks came in a Tuesday statement marking the 99th anniversary of the foundation of Iraq's Armed Forces.
"The Iraqi army currently includes only six Turkmen officers," he said, adding that such blatant under-representation was "incompatible with the constitution".
Article 9 of Iraq's national charter states that the Iraqi Armed Forces and security services "should be drawn up from components of all the Iraqi people… without discrimination or exclusion".
After Arabs and Kurds, Turkmen represent Iraq's third largest ethnic community.
There are no official figures for Iraq's total Turkmen population, but Turkmen officials say they account for about 7 percent of the country's population of 38 million.