The Iraqi parliament earlier this week voted against plans by leaders of the autonomous Kurdish region in northern Iraq to hold the non-binding September 25 referendum.
On June 7, Barzani announced his intention to hold a referendum on the independence of the Kurdish region from Iraq on September 25.
Washington reiterated its opposition on Friday, with the White House saying in a statement that it was concerned that holding the referendum in disputed areas is "provocative and destabilizing" and calling on Kurdistan's regional government to call it off.
The United States has proposed unspecified "alternatives" to the poll.
Germany also renewed its opposition to the unilateral independence referendum.
"The United Nations might get involved in the controversy over the KRG's independence referendum plans in the upcoming days", he said.
"The referendum risks increasing instability in the region when the focus should be on defeating Daesh", said the statement, making a reference to an ongoing fight against Takfiri terrorists in Iraq.
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The UK Foreign Office said in order for the Iraqi Kurds to settle their disputes with the central government, they had better engage in dialogue with Baghdad and set aside plans for independence.
The referendum is planned to be held in Kurdistan and disputed areas including the oil-rich province of Kirkuk.
The parliament met in the KRG capital, Erbil, in northern Iraq.
"We've been waiting more than 100 years for this", Omed Khoshnaw, a lawmaker from the Kurdish Democratic Party (KDR) of KRG President Massoud Barzani said.
"Those assembled in parliament today think this is a lawful session, but this is unlawful", Birzu Majeed, the head of Gorran's parliamentary block, told a news conference held while parliament was in session.
Kirkuk has always been the center of dispute between Baghdad and the Kurds, raising the prospect that conflict could erupt between Arabs, Turkmen and Kurds.
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.