In a speech to parliament on Wednesday, Mr Abadi reiterated his order that the Kurdistan Regional Government (KRG) must give up control of its international airports by Friday, or face a ban on international flights into the Kurdish region. Kurdish forces must also withdraw from disputed areas currently under KRG control such as Kirkuk, he added.
Northern Iraq's 8.4 million strong population voted overwhelmingly in favour of independence in Monday's referendum, which was non-binding and not recognised by Baghdad's central government. It is believed to have returned a 90 per cent 'yes' result on a turnout of approximately 72 per cent.
"We won't have a dialogue about the referendum outcome," Mr Abadi told assembled politicians. "If [the KRG] want to start talks, they must cancel the referendum and its outcome."
The Kurdish people – who number roughly 30 million across several countries – were left stateless when the Ottoman Empire collapsed a century ago.
While the vote was been met with enthusiasm by the Kurdish diaspora all over the world, Baghdad and Iraq's Arab population have expressed their concerns that areas voting in the referendum include Kirkuk, an ethnically mixed and oil-rich province.
Ths US also repeatedly attempted to persuade the KRG to delay the referendum, fearing further friction between Irbil and Baghdad could derail the fight against Isis and Iraq's fragile peace.
The Iraqi Civil Aviation Authority sent a notice on Wednesday to foreign airlines telling them international flights to Erbil and Sulaimaniya in the Kurdish region would be suspended on Friday at 1500 GMT.
KRG Transport Minister Mowlud Murad rejected Baghdad's instructions, telling a media conference that the airports must remain open to maintain the Kurdish economy and to facilitate the offensives on Isis' last remaining strongholds in the country.
The move comes after neighbouring Turkey and Iran closed their airspace as voting took place on Monday.
Ankara and Tehran are worried that the creation of an independent Kurdistan could fuel the desire for Kurdish independence within their own countries.
Turkish President Recep Tayyip Erdogan sent troops and tanks to the border with the KRG earlier this week, where they were joined for joint exercises with Iraqi troops.
The Turkish leader has accused KRG President Masoud Barzani of "treachery" in going ahead with the independence referendum, warning on Tuesday that Iraq's Kurds would starve if Turkey decided to close its long border with northern Iraq.
Further economic and military action were both options on the table for Ankara, he added, if Turkey's security was threatened by the outcome of the independence referendum.
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