GENEVA (Reuters) - U.S. Secretary of State Rex Tillerson said on Thursday Iraq must stand on its own in the face of Iranian influence, while recognizing that the two states shared a long border and legitimate economic interests. Tillerson, who held talks with Iraqi Prime Minister Haider al-Abadi in Baghdad this week, was asked by reporters in Geneva about blunting Iran s influence.  What we are saying to the Iraqis is you must develop the capacity to stand on your own, he said. The United States remained very concerned about the fighting  that has erupted between Iraqi security forces and the Kurdish peshmerga militia over the Kurdish independence referendum, Tillerson said. He said that the United States was  disappointed that the parties have been unable to reach an entirely peaceful resolution  and that he had encouraged Abadi  to accept Erbil s (the Kurdistan regional government s) overtures for talks on the basis of the Iraqi constitution . 