(Recasts with more quotes) BAGHDAD, Jan 3 (Reuters) - A U.S. general said on Wednesday U.S. forces had no role in Saddam Hussein's hanging but would have handled it differently, after a video of Iraqi officials taunting him on the gallows sparked outrage among Sunni Arabs. "Had we been physically in charge at that point we would have done things differently," U.S. military spokesman Major General William Caldwell told a news conference in Baghdad. Caldwell said U.S. forces, who had physical custody of Saddam for three years, left all security measures at Saddam's execution, including searching witnesses for mobile phones, to Iraqi authorities. Reacting to criticism of the hanging that has embarrassed U.S. officials, moderate Shi'ites and ethnic Kurds, Caldwell urged the Iraqi government to reach out to disillusioned Sunni Arabs. "At this point the government of Iraq has the opportunity to take advantage of what has occurred and really reach out now in an attempt to bring more people back into the political process and bring the Sunnis back," he said. An unofficial video of the hanging, apparently filmed on a mobile phone, showed Shi'ite officials mocking Saddam just before he was hanged, inflaming sectarian passions in a country already on the brink of sectarian civil war. Asked about criticism of the hanging, Caldwell said: "We had absolutely nothing to do with the facility where the execution took place." "We've only had physical control and so all we did was return physical control of him back to the Iraqis who've always had the legal custody of him. At that point it's a sovereign nation. It's their system, they make those decisions." He said U.S. forces flew Saddam to the prison where the execution took place at dawn and then withdrew from the building. They were not responsible for searching the witnesses for phones, he said. The Iraqi government has promised an investigation into how a witness at the hanging filmed it on a mobile phone and released the video to television stations and Web sites.