On Wednesday, the US daily said that Washington had serious and credible reports from Iraq concerning acts of abuse in autonomous Kurdish areas.
US officials, it said, had expressed serious concern over reports that hundreds of Arabs and Turkmens had been abducted in the city of Kirkuk and hauled off to prisons in Arbil and Sulaimaniyah.
Kurds want the oil-rich city to be the capital of their northern region and to reverse an Arabisation policy carried out there by the regime of former Iraqi president Saddam Hussein.
The Post quoted State Department spokesman Sean McCormack as saying: "These allegations and these reports are very serious concern to us, and we have raised our concerns in a forthright way with the authorities involved or who we believe to be involved."
McCormack did not cite the Kurds specifically, but a department official who asked not to be named confirmed the allegations focused on the Kurds.
On Monday, Barzani said: "The Americans arrest suspects in Kirkuk and other regions and asked to send them to Arbil for a specific length of time until interrogations have been completed or until US forces took them back again."
He did not say who carried out the interrogations.
"We did not arrest anyone, and those transferred to Arbil were at the insistent request of the Americans, who subsequently took them back."
McCormack had formally denied any US implication in the matter.
"Our coalition forces, according to every report that I have, not only were not involved in these activities, but in fact, raised their concerns about the fact that they had serious and credible reports" about them, he said.