Iraq's central government rejected the vote, saying it violated the constitution.
Iraqi Kurdish authorities said Tuesday they will respect a Supreme Court decision banning secession.
Iraqi President Fouad Masoum called for dialogue between the Iraqi central government and the Kurdistan Regional Government (KRG) to overcome political and security problems after the KRG's independence referendum on September 25.
"We believe that this decision must become a basis for starting an inclusive national dialogue between Erbil and Baghdad to resolve all disputes", the KRG said in a statement.
The ruling responded to a request from the Iraqi government in Baghdad to put an end to any "misinterpretation" of the constitution and to "assert the unity of Iraq", a court spokesman said last week. Iraqi army conducted joint exercise with Turkish army along the Iraqi Kurdistan border.
The referendum was conducted at a time when Iraqi army was engaged in a military campaign to retake the territories rune over by Kurdish Peshmarga militants in the course of the fight against Daesh (IS).
Abadi had previously urged the northern semi-autonomous Kurdish region to abide by the court's decision.
Russian Foreign Minister Sergi Lavrov after receiving the Iraqi Foreign Minister Ibrahim al-Jaafari, in a press conference on October 23, said that his country was not closing its consulate in the capital of the Kurdistan Region, but that the mission was nevertheless subordinate to the Russian Embassy in Baghdad.
The Iraqi Foreign Ministry stated on Monday that it can not shut down the diplomatic offices and consulates of the foreign countries in the Kurdistan Region because they are not political.
"We've had for many years a very good relationship with the Kurds as you know and we've also been on the side of Iraq, even though we should have never been there in the first place", Trump told reporters at the the White House, according to Reuters.