The timing of the September 25 vote has drawn criticism from both the Baghdad and Western governments, coming as the campaign against the Islamic State jihadist group in Iraq if still unfinished.
In a telephone call yesterday, US Secretary of State Rex Tillerson said Washington "would want for the referendum to be postponed and that the issues between the Kurdistan region and the federal government in Baghdad should be addressed through dialogue", Barzani's office said in an English-language statement.
Some Iraqi Kurdish officials have openly acknowledged that calling the referendum was intended as a bargaining counter in negotiations with Baghdad on other issues.
The Kurdish regional government's representative in Iran, Nazem Dabbagh, said last month that the Kurds wanted Baghdad to meet their longstanding demand for plebiscites on incorporating other historically Kurdish-majority areas in their autonomous region.
He said they also wanted Baghdad to ratify laws on oil revenues and funding for the Kurdish security forces, known as the peshmerga, who have played a crucial role in the fight against IS.