Official preliminary results said 93 percent of voters backed Kurdish independence, although the vote was widely criticized by the worldwide community. The officials spoke on condition of anonymity to discuss the plan.
The result was a resounding 92.7 per cent "yes" for independence.
Calling the vote "unconstitutional", Iraq's parliament on Wednesday also asked Abadi to send troops to the oil-producing, Kurdish-held region of Kirkuk to take control of its lucrative oil fields.
Some Turkish analysts predicted that Turkey can go further to intervene militarily to safeguard the rights of the Turkmen minority living in Kirkuk, one of the contentious cities located in northern Iraq.
"Prior to the vote, we worked with both the KRG and the central government in Baghdad to pursue a more productive framework and to promote stability and prosperity for the people of the Kurdistan region".
Information for this article was contributed by Bradley Klapper and Robert Burns of The Associated Press; by Rod Nordland and David Zucchino of The New York Times; and by Mustafa Salim, Karen DeYoung, Tamer El-Ghobashy and Aaso Ameer Schwan of The Washington Post.
Abadi's office said the Kurdish region's two global airports, in Irbil and Suleimaniya, could be reopened as soon as Kurdish officials transferred control of them to the federal government.
Turkish carriers Turkish Airlines, AtlasGlobal and Pegasus were set to halt flights to and from airports in the Kurdish region on Friday, in line with a ban announced by Baghdad following an independence referendum held by Iraq's Kurds earlier this week.
Thursday's decision saw people, many of them foreigners, turn out in droves at Arbil airport to avoid getting stuck in the autonomous Kurdish region of northern Iraq. But he added his demand that the Kurdistan Region cancel the vote in order to give relations between Baghdad and Erbil a fresh start.
"We assure the global community of our willingness to engage in dialogue with Baghdad", he said, insisting the referendum was not meant "to delimit the border [between Kurdistan and Iraq], nor to impose it de facto".
Most worldwide carriers who fly to and from airports in the Kurdish region announced they would halt flights beginning tonight in line with the ban.
The ban on global flights servicing airports in the Kurdish region is set to go into effect.
Analysts say that despite their threats, Baghdad, Ankara and Tehran are wary of sparking a serious confrontation with the Kurds.