Still, it warned that the vote is likely to have repercussions for the KRG and its relations with Baghdad and its neighbors.
"We believe this step will increase instability and hardships for the Kurdistan region and its people," State Department spokeswoman Heather Nauert said in a statement.
"The fight against ISIS is not over, and extremist groups are seeking to exploit instability and discord. We believe all sides should engage constructively in a dialogue to improve the future of all Iraqis," she added, referring to the Islamic State of Iraq and Syria, or Daesh.
A spokesman for the UN Secretary General said in a separate statement that Antonio Guterres "regrets that the opportunity for serious negotiations to resolve outstanding issues between the Government of Iraq and the Kurdistan Regional Government, based on the Constitution and in a spirit of partnership and mutual respect, were not fully seized prior to this move".
"The decision to hold the referendum in disputed areas, notably in Kirkuk, is particularly destabilizing," Stephane Dujarric said.
Monday's non-binding referendum took place in KRG-held areas in northern Iraq, including areas disputed between Erbil and Baghdad.
The referendum, which was boycotted by Turkmens and Arabs, was held in Erbil, Dohuk and Sulaymaniyah provinces, the contested province of Kirkuk, Tuz Khurmatu district in Saladin province and Khanaqin district in Diyala province.
The final results of the controversial poll, in which roughly 72 percent of eligible voters cast their ballots, are expected within three days.
Earlier Monday, Turkish President Recep Tayyip Erdogan said Turkey would take political, economic, commercial and security steps against the KRG.
Iraq’s central government has threatened to intervene militarily if the vote leads to violence.