Iraqi authorities said on Tuesday they were lifting a almost six-month air blockade imposed on Iraqi Kurdistan in response to its holding of an independence referendum.
A statement by his office said Abadi signed a decree to lift the ban after receiving positive response from the Kurdish local authorities "to restore the federal authority in the two airports in accordance with the Constitution of Iraq".
In Iraq, airports in the country's Kurdish region will be opened to global flights after federal authority has been restored.
Baghdad imposed the blockade in September after Iraqi Kurdistan voted for independence in a non-binding referendum.
Al-Abadi said a higher committee will be formed "to oversee the management of the Kurdish region's airports to ensure their compliance with the federal government's standards".
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Kurdish authorities confirmed that airports in Iraqi Kurdistan will return to federal Iraqi control and would report to Baghdad's Interior Ministry.
"This will depend on how long it takes for employees of the central government to start working in the airports", he said.
It also specified that the biometric system used in the Kurdistan Region's airports will be linked with the federal system.
This prompted Baghdad to impose a raft of punitive sanctions on the KRG, including a ban on worldwide flights into and out of the Kurdish region.
Arbil had already agreed to that and control of airport security was the last stumbling block, an official told AFP at the end of February when the blockade was extended for another three months. Around 25 million Kurds live in a territory that spans the borders of modern-day Turkey, Iraq, Syria, Iran and Armenia.