The move eases tensions between the federal and regional governments, paving the way for a lasting settlement as well as possible increased cooperation against jihadists they are both fighting.
"The Iraqi finance ministry... On Wednesday transferred the amount of 583 billion Iraqi dinars, which equals USD 500 million, to the account of the regional government," Hoshyar Zebari told a news conference.
Upholding its side of the deal to transfer 150,000 barrels of crude per day to Baghdad's control, the three-province Kurdish region began moving oil to federal oil tanks in the Turkish port of Ceyhan yesterday, Zebari said.
Baghdad has long opposed the Kurdish region's independent export of oil, while Kurdish leaders have sharply criticised Baghdad for withholding budget payments to the region for much of this year.
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"From March until now, this is the first financial payment to go to the region," Zebari said.
The two sides are also at odds over control of a swathe of northern territory that the Kurds want to incorporate into their autonomous region, a move Baghdad strongly opposes.
In praising the deal, Oil Minister Adel Abdul Mahdi had previously said that it eases a dispute "that threatens not only economic, security and political interests, but also threatens national unity."
It comes at a time when both federal and Kurdish forces are battling jihadists of the Islamic State group, which spearheaded an offensive that has overrun large areas of the country since June.