US Vice President Dick Cheney made a surprise visit to Iraq on Sunday, touring the country after parliamentary elections that he suggested were a major step toward withdrawing US forces. "The participation levels all across the country were remarkable," Cheney told reporters after an hourlong briefing from the war's top US military commanders. "And that's exactly what needs to happen as you build a political structure in a self-governing Iraq that can unify the various segments of the population and ultimately take over responsibility for their own security." The high-security daylong tour was so shrouded in secrecy that even Iraq's prime minister said he was surprised when he showed up for what he thought was a meeting with the US ambassador only to see Cheney waiting to greet him. Cheney's tour of the country came on the same day that US President George W. Bush was to give a prime-time Oval Office address to US on Iraq. Cheney's aides said the timing was a coincidence but regardless, the two events combined in a public relations blitz aimed at capitalizing on the elections to rebuild support for the unpopular war.