President Jalal Talabani, a Kurd, has held the position since 2006, but his term is at an end, leaving the question of who will succeed him in doubt.
In recent years, a de facto agreement has emerged whereby the president has been a Kurd, the premier a Shiite Arab and the speaker of parliament a Sunni Arab.
The federal presidency "is a right of the people of Kurdistan, and we affirm this right to the Kurdish people," the region's presidency said in an online statement.
And it said that any nominee for the post must be approved by the Kurdish regional parliament -- a demand almost certain to draw the ire of Arab politicians.
The claim over the post is seen by Kurds as an important symbol after decades of central government oppression before the US-led invasion of 2003.
It is also a link between their three-province autonomous region and Baghdad, which are at odds over various long-running disputes.
The constitution, however, does not mandate that the posts be distributed along religious and ethnic lines.
The new premier is all but guaranteed to be drawn from Iraq's Shiite majority again following the April 30 election, but who will fill the other two positions is still undecided, with a Sunni Arab or a Kurd potential options for both.
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