The White House urged Iraq's Kurdish leaders to cancel the September 25 vote on independence, saying the move is a distraction from the efforts to defeat Daesh.
Baghdad has repeatedly opposed the Kurdish referendum, calling it "unconstitutional".
"To this date, we have not received an alternative that can take the place of the referendum".
An worldwide delegation, including the United States, Britain and UN envoys, met with Barzani and presented the alternative path for the controversial independence referendum.
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The referendum is planned to be held in Kurdistan and disputed areas including the oil-rich province of Kirkuk.
The region's vice-president Jaafar Aimenky, who chaired the session, announced the poll would go ahead after 65 out of 68 lawmakers present voted in favour.
The regional parliament's decision came despite an intense diplomatic drive by the United States, which has provided critical military aid to the KRG's fight against Daesh, to persuade the Kurdish leadership to cancel the referendum.
This week, top U.S. envoy Brett McGurk was again in Arbil and attempted to persuade the Kurdish leader to call off the highly-charged popular vote in exchange for a new diplomatic initiative.
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Neighbouring Turkey and Iran fear the referendum could stoke separatist aspirations among their own sizeable Kurdish minorities.
Under this plan, a well-placed source told AFP, the worldwide community will oversee negotiations on revenue sharing in Iraq's oil budget and payment for Kurdish militia fighters.
Turkey is furious about the referendum, with loyalists to President Recep Tayyip Erdogan even whipping up anti-Semitic fake news stories claiming that the Kurds have a deal with Israel to flood Kurdistan with Jews.
Baghdad recognises Kurdish autonomy in some areas of Iraq but the precise boundary of the Kurds' self-ruled region and the rest of the country is disputed.
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