Differences over the disputed oil-rich Kirkuk province have still not been settled, so it too has had to be left out.
BBC: Local polls pose challenge for Iraq after US withdrawal
Sunni anger exploded this week over security force actions in the Kirkuk province city of Hawija this week that led to deaths.
Mr Maliki has questioned the Kurds' right to control some of the disputed areas, for instance around the town of Khanaqin and in some parts of Kirkuk province.
As before, they are sure to demand de facto independence, autonomy over finance, control over Kirkuk province, a fixed percentage of Iraqi revenues, and even control over Kurdistan's minerals.
Tensions have grown in recent months between Iraq's Sunnis and Shiites, especially after an incident last month in Hawija, in Kirkuk province, where Iraqi security forces raided a site used by Sunni protesters to demonstrate against the Shiite-led government.
Tensions have grown in recent months between Iraq's Sunnis and Shiites, especially after an incident in Hawija, in Kirkuk province, last month where Iraqi security forces raided a site used by Sunni protesters to demonstrate against the Shiite-led government.
CNN: Tribal fighters clash with Iraqi army amid rising tensions
But most Kurds do demand fat chunks of extra territory, especially but not only in Kirkuk province, which they were deprived of by Saddam when he Arabised Kurdish lands by expelling Kurds and bringing in Arab settlers from Iraq's south and centre.
In the northern province of Kirkuk, the object of a highly charged ethnic conflict, security forces went on maximum alert.
No vote is scheduled in the ethnically disputed province of Kirkuk, which has not had a chance to elect local officials since 2005 because residents cannot agree on a power-sharing formula there.
Antiriot security forces attacked the Hawija protest camp during the early morning hours of Tuesday, according to security officials in the restive province of Kirkuk, killing 25 people, burning tents and arresting 75 protesters.
The Kurds were especially chuffed by early election results for a provincial council (outside their present self-rule area) in the disputed province of Kirkuk, which they look set to dominate with a reported 60% of the vote.
However, given the deep differences between Shias, Kurds and others over the role of Islam, the extent of federalism and the status of the disputed province of Kirkuk, the government may have to invoke a law that allows for a six-month extension, beyond the August deadline.
So his departure could hurt the chances of resolving the Arab-Kurdish dispute over land and oil in the border region around Kirkuk, a city and province which the Kurds say is theirs.
Legislators overcame an impasse over a key provincial elections law last month by setting the problem of Kirkuk aside and deciding to exclude the province from a vote expected early next year.
The nation's three Kurdish provinces will hold elections in May, and voting in Tameem province has been suspended because of political disputes in Kirkuk.
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