The military authorities in Iraq are offering a $25m reward for information leading to the capture of former president Saddam Hussein.
There are suggestions Saddam Hussein could be hiding in Baghdad
The top US official in Iraq, Paul Bremer, said $15m was being offered for similar information about Saddam's two sons, Uday and Qusay.
"I have certainly not forgotten Saddam Hussein and his sons," Mr Bremer said in a message broadcast to the Iraqi people.
"They may or may not still be alive. Until we know for sure, their names will continue to cast a shadow of fear over this country."
Meanwhile, two Republican senators who visited Iraq this week said they were party to classified material which left them in no doubt that Saddam Hussein did possess weapons of mass destruction.
Pat Roberts, chairman of the Senate Intelligence Committee, told a news conference that troops had found "what I would call breakthrough pieces of information that I hope in the near future will be very positive news".
The whereabouts of Saddam Hussein has been the source of much speculation since Baghdad fell to US-led forces on 9 April.
STRIKES ON SADDAM
20 March - In the opening hours of the war, US air strikes target a Baghdad compound where Saddam Hussein is believed to be staying
7 April - Air strikes hit Baghdad's Mansour district amid reports that Saddam Hussein and his two sons are meeting in a restaurant
18 June - US forces attack a convoy near the border with Syria that may have been carrying Saddam Hussein and at least one of his sons
The BBC's Richard Galpin in Baghdad says the capture or death of the deposed Iraqi leader and his sons would have much more than just symbolic value.
The United States and UK believe the fact they are still at large provides a motive for members of the former regime to continue a wave of attacks against the US-led troops.
Our correspondent says those responsible for the violence may believe there is a chance of forcing the American and British troops out so that the old regime can return to power.
"We believe it is important to do everything we can to determine his (Saddam Hussein's) whereabouts, whether he is alive or dead, in order to assist in stabilising the situation and letting the people of Baghdad be absolutely sure that he is not coming back," US Secretary of State Colin Powell told reporters in Washington.
Mr Bremer has said the failure to capture or kill the deposed president is hampering coalition efforts to control the country.
At least eight US soldiers were wounded in three separate attacks on troops on Thursday.
US troops have been frequently targeted in Iraq
In the most serious incident, the US military said a two-vehicle convoy had been targeted by "an explosive device" which wounded six soldiers in Ramadi, 100 kilometres (60 miles) west of Baghdad.
Troops on patrol in central Baghdad also came under fire, with one soldier sustaining injuries before the gunman was shot dead. A six-year-old Iraqi boy was wounded.
At least 18 US and six British troops have been killed by hostile fire since US President George W Bush declared major combat in Iraq over on 1 May.
Last month, US forces attacked a convoy near the border with Syria that was believed to have been carrying senior members of the former Iraqi regime.
It was unclear whether Saddam Hussein was in the convoy, but US officials were reported to have carried out DNA tests on the victims.
At least two US airstrikes targeted Saddam Hussein during the war but there has been no confirmation of their success.