U.S. Secretary of State Rex Tillerson made the request Friday, during a phone call with the president of Iraq's Kurdistan Regional Government, Massoud Barzani.
The U.S. State Department said in June it was concerned that the referendum will distract from "more urgent priorities" such as the defeat of Islamic State militants.
"On the issue of the postponement of the referendum, the President (Barzani) stated that the people of the Kurdistan Region would expect guarantees and alternatives for their future," said the statement issued by the Kurdish presidency after Tillerson's call, giving no further details on the Kurdish leader's reaction to the U.S. request.
The United States and other Western nations are concerned that the vote could turn into another regional flashpoint.
Turkey, Iran and Syria, which together with Iraq have sizable Kurdish populations, all oppose an independent Kurdistan.