US Defence Secretary Donald Rumsfeld promised Iraqis that US troops would stay on until they have eliminated all vestiges of Saddam's regime. In a broadcast on coalition-run Al-Iraqiya television during an unannounced visit to the capital Saturday, the hawkish US defence chief said the American military would fight on in Iraq until Saddam's reign of "terror" was history. But the rebel chief said the fugitive former president was personally directing the insurgency still dogging US troops eight months after they entered the Iraqi capital. Saddam Hussein is in good health and living in the west of Iraq," said the man who is involved in the struggle and calls himself only Abu Mohammed. "The Iraqi president is commanding the military operations against the American forces," he said.