The move came after Iraq's parliament voted to remove the governor of Kirkuk, a staunch supporter of Kurdish independence.
Kurdish leaders will study a western delegation's plan to delay the autonomous region's planned referendum on independence, according to a statement from the Kurdish presidency.
With the presence of 68 MPs out of 111, the Kurdistan Parliament in a unanimous vote mandated the Independent High Election and Referendum Commission (IHERC) to hold the independence referendum on September 25.
Critics of the vote, including the United States and the European Union and even some members of Iraq's 5.5 million-strong Kurdish minority, say it could distract from the fight against jihadists.
"To this date, we have not received an alternative that can take the place of the referendum", Barzani told a pro-referendum rally in Amedi on Friday, Rudaw reported.
The prime minister said he is expecting to see new developments regarding the issue after the U.N.'s possible involvement.
"Heading into a referendum for September 25, there is no prospect for worldwide legitimacy", Brett McGurk, a US special envoy, told reporters after a delegation also including the United Nations and Britain met Kurdish President Massoud Barzani. It is clear that the Iraqi authorities can maximally grant a broader autonomy to the Iraqi Kurds seeking independence.
Turkey's Recep Tayyip Erdogan has advised his Iraqi Kurdish counterpart Massoud Barzani to back off from plans to host a referendum on Iraqi Kurdish independence.
Turkey and the USA are also opposed to the vote.
Kurds have long claimed Kirkuk and its huge oil reserves.
The neighboring countries of Turkey, Iran and Syria also feel that the move would threaten their territorial integrity, as large numbers of Kurdish population live in those countries.
But Kurdish region President Masud Barzani has said the vote is necessary because "all other bids" to secure full Kurdish rights "have failed".
But the ethnically mixed city also has Arab and Turkmen populations.
With the exception of Israel, nearly all Western countries friendly to the Iraqi Kurds have publicly opposed the Kurdish referendum.