The offer was made in a statement released by the US occupation authority in Iraq on Thursday which also offered a US$15 million bounty for information on either of Saddam's two sons, Oday and Qusai.
The bounty offer came at a time of increasing resistance attacks against US and British forces in Iraq which American officials have blamed on supporters of the ousted leader.
"If any of you has such information, I encourage you to come forward and give it to any coalition official - civilian or military," US administrator for Iraq, Paul Bremer said in the statement.
"They may or may not be alive. But I recognise that, until we know for sure, their names will continue to cast a shadow of fear over this country," he said.
Saddam was last reportedly seen alive in the days leading to the end of the war in the Azamiyah neighborhood of northeastern Baghdad.
The US military has said at least two airstrikes targeted him during the war but it is not known if any were successful.
In the latest resistance operation, US troops came under fire in the town of Ramadi, west of Baghdad, local residents said early Friday, but there was no word on casualties.
Two loud explosions were heard in the area of the former intelligence services base around three kilometers outside Ramadi where US troops are stationed, witnesses said.
A US Humvee light vehicle was also hit by rocket-propelled grenades on al-Attubaa central street around the same time, they said.
Residents of the town of Fallujah, further down on the highway leading to Baghdad, also reported US troops had fanned across the streets in a state of alert after the Ramadi attacks.
Rising casualty toll
At least 10 US soldiers were wounded and three Iraqis killed in four incidents in Iraq on Thursday, a day after US President George W Bush defiantly vowed that resistance attacks would not drive out American troops.
US occupation troops come under
almost daily resistance attacks
A rocket-propelled grenade launched in central Baghdad wounded at least three US soldiers, said American military officials.
Eyewitnesses at the scene said the soldiers opened fire on a car killing the driver and wounding several civilians standing nearby.
US military officials confirmed the Iraqi civilian was killed without giving any further details.
The resistance fighters also threw a hand grenade at the military vehicle before setting it on fire with gasoline.
In Ramadi, six US soldiers were also injured when an "explosive device" targeted their two-vehicle convoy, according to military sources.
Residents of the town, 100 km west of the capital, said two men on a motorbike fired a rocket-propelled grenade at a military convoy.
In the northern Baghdad neighbourhood of Kadhimyah, another US patrol came under fire, leaving an American soldier and a six-year-old boy injured. The Iraqi resistance fighter was killed.
Bush vowed US troops would not
be driven out of Iraq
In Baquba, 60 km northeast of Baghdad, an Iraqi was killed when a bomb exploded during a protest against the arrest of a Shia cleric.
In a move likely to incease tensions, US forces opened fire at demonstrators, injuring at least four.
US soldiers arrested Shia cleric Ali Abd ul-Karim al-Madani on Thursday in Diyala province.
Our correspondent said soldiers stormed the prominent cleric's home, seizing eight of his sons and aides.
Troops defile Quran?
Eyewitnesses told Aljazeera TV soldiers threw the Quran, Islam's holy text, on the floor during the raid.
Thousands of people in Baquba took to the streets.
In a separate incident, a US soldier was killed in a "non-combat incident" on Thursday, according to a military statement. No further details were given.