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The ministry said it had formed a management team to handle production after Shell exits the field by the end of June.
"The priority of the new management team is to cut the cost of producing a barrel (of crude) from Majnoon by 30 percent," Oil Minister Jabar al-Luaibi said in a statement.
Iraq plans to increase output from Majnoon to 400,000 barrels per day in the "coming years," the ministry said, without giving a precise timeline.
Production is now about 235,000 bpd, oil officials say.
A letter signed by the minister, dated Aug. 23 and seen by Reuters, gave approval for the Anglo-Dutch firm to quit Majnoon, a major oilfield near Basra which started production in 2014.
Shell said it would focus its efforts on developing and expanding Basra Gas Company in Iraq after handing over operations of Majnoon to the Iraqi government.
Basra Gas Company is a joint venture between Shell, South Gas Company and Mitsubishi and the Petrochemical Project NEBRAS.
Chevron, Total and PetroChina may form a consortium to develop Iraq's Majnoon oilfield, the minister said in Vienna in November.