Global flights to and from the region's two main airports have been halted since September 29, part of sanctions imposed on the semi-autonomous Kurdistan region after it conducted an independence referendum in defiance of Baghdad's wishes.
Iraqi Prime Minister Haider al-Abadi said Tuesday the airports of Arbil and Sulaimaniyah were "again open to worldwide flights" after the federal authority was restored at the hubs.
The prime minister said the ban was lifted "after local authorities in the Kurdish region accepted the return of the two airports to the federal authority".
Since the air ban was enforced, all Kurdistan-bound worldwide flights have been rerouted to Baghdad, which has also imposed entry visas to foreigners wishing to visit the Kurdistan region.
"Kurdistan's regional airports will be under the command of the Federal Ministry of the Interior", the statement said. The move followed an agreement with Kurdish officials to put their two airports under federal control.
Iraqi President Fuad Masum has refused to approve the 2018 national budget law and returned it to the Iraqi Parliament for amendment, the President's Media Office said in a statement on Tuesday.
It also specified that a biometric system used in Kurdistan's airports will be linked with the federal system.
The Iraqi President has rejected the 2018 national budget law, approved by the Iraqi Parliament after a majority vote, due to the presence of constitutional violations in the bill.
The budget cut the Kurds' share from the 17 percent the region has traditionally received since the fall of Saddam Hussein.
In a previous draft the KRG portion was set at 12.67 percent, which is how much of Iraq's population Baghdad says the provinces in Kurdistan make up.