The comments, by Deputy Secretary of State Richard Armitage, appeared to signal that only clean surrender could guarantee survival to the former Iraqi dictator.
"If Saddam Hussein could be captured safely, without any harm to US service persons, that would be great," Armitage told CNN television.
"If there is a question of harm being done to US servicemen, then he should be killed".
The deputy secretary of state became the second high-ranking US official to indicate in less than a week that while the US was interested in getting Saddam out of the picture, it had no particular concern whether he ended up alive or dead.
Speaking in Congress last Wednesday, Defense Secretary Donald Rumsfeld said top Pentagon officials had left it to commanders in the field to decide whether to take former senior Iraqi leaders dead or alive.
"If a person is determined to fight to the death, then they may very well have that opportunity," Rumsfeld warned without specifically mentioning Saddam Hussein.
The remarks by Armitage came a week after US forces killed Saddam Hussein's two sons, Uday and Qusay, following a pitched battle in the northern Iraqi city of Mosul, a breakthrough that led to an intensified the search for the deposed strongman.
Three US soldiers were wounded in that operation, according to defense officials.
With the hunt for Saddam gathering steam, Armitage insisted that US troops in Iraq were now hot on his trail and stood a good chance of catching up with him.
"I think most people feel that the noose is tightening pretty regularly around the neck of Saddam Hussein," he said.
"Even today, there were three raids. And we believe we were just hours behind Saddam Hussein. So it looks like his days are numbered".
But Captain Jeff Fitzgibbons, a spokesman for coalition forces in Baghdad, told AFP the military had no evidence that capture of the former Iraqi leader was imminent.
"I don't have any hard facts in my possession that would indicate that was the case," Fitzgibbons said in a telephone interview. "I do know that they talked to some locals that felt he had just been through, but there is nothing really confirmable as far as facts that would lead us conclude irrefutably that that was the case". – Sapa-AFP.
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