The exercises, involving tanks and armored vehicles, continued on Friday.
"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".
Meanwhile, Turkish Foreign Ministry issued a notice barring representatives of the Kurdistan Regional Government (KRG) from returning to Turkey.
In a phone call with Abadi, Turkish Prime Minister Binali Yildirim "confirmed the support of his country to all decisions" taken or sought by the Iraqi government in Baghdad after the independence referendum held in Iraqi Kurdistan on Monday, Abadi's office said in a statement.
Although the Kurdish region in northern Iraq already has a considerable degree of autonomy from Baghdad, its voters this week endorsed a nonbinding resolution calling for independence by a margin of 92.7 percent.
Barzani said last week one reason for holding the referendum was because he feared Iraq, split between a Shi'ite majority and Sunni minority, was becoming a sectarian-based "theocracy", not a proper democracy as promised after the 2003 US -led invasion that ousted veteran ruler Saddam Hussein.
Turkey has threatened to close down an oil pipeline used by Kurdistan for exports. Turkish President Tayyip Erdogan said the Kurdish government must be prevented from making "bigger mistakes".
Clashes between Iranian security forces and the Iranian Kurdish militants based in Iraq are fairly common in the region, with Kurdish separatists regularly carrying out cross-border attacks on Iranian forces.
That's according to a late Wednesday night report by the state-run Qatar News Agency.
"This involves border claims, military action directed against (Iraqi city) Kirkuk and the pressure on airlines to cease operations into the Kurdistan Regional Government".
However, the analyst noted that the KRG held the referendum beyond the realm of pragmatism, because the Kurds knew that "if the oil is really cut off and if Erdogan really follows through on this threat, the economy will collapse in quick order".
He underlined that Ankara has no problem with its "Kurdish brothers", as Turks, Kurds, and other ethnic groups are living in unity and fellowship in Turkey. Behind the scenes, the USA has strongly been advising against any military incursion into the Kurdish region and believes none of the players will do so, said the officials, who spoke on condition of anonymity because they weren't authorized to speak publicly on the matter.
He said that cutting off the Kurdish region's trade with Turkey, which he said totals $17 billion a year, would hurt everyone. That's something, at least, since Iraq, Iran, and Turkey all seem to be preparing war against Kurdistan to bring it back under Baghdad's thumb.
In Turkey, which hosts the majority of Kurds, the PKK has been engaged in an armed campaign for autonomy since 1984, which has led to more than 40,000 deaths.