The United States will work with the people of Iraq to ensure the trial of Saddam Hussein stands international scrutiny, President George W Bush says.
The US said Saddam Hussein offered no resistance
The deposed Iraqi leader will get the justice he denied to millions, Mr Bush told a news conference in Washington.
Mr Bush said it was for Iraqis to decide whether Saddam Hussein should face the death penalty.
The ex-leader has reportedly given no direct intelligence to interrogators since being captured at the weekend.
But US military officials say two key figures have been arrested on the basis of information "gleaned" from Saddam Hussein's capture.
"The Iraqis need to be involved," Mr Bush said when asked what will now happen to Saddam Hussein.
"There needs to be a public trial and I'm confident it will be done in a fair way."
Mr Bush did not say whether Saddam Hussein should eventually face execution.
"This is a brutal dictator...But my personal views are not important in this matter...It's going to be up to the Iraqis to make those decisions."
He also said the work of US-led forces in Iraq remained difficult and would require further sacrifice, but Iraq was on the path to
These words echoed those of UK Prime Minister Tony Blair, who warned that what he called "terrorists and Saddam's sympathisers" would continue their operations despite Saddam Hussein's capture.
Underlining US and UK warnings, two car bombs exploded in Baghdad on Monday, killing at least eight people.
Hours later, violence erupted in the flashpoint town of Falluja where pro-Saddam demonstrators stormed the regional government offices.
Journalists at the scene told the French news agency AFP that demonstrators broke into the building, put up portraits of Saddam and set furniture alight.
The US military said it had identified a militant cell in Baghdad and arrested two key anti-coalition figures.
Brigadier General Mark Hertling told AP news agency that the arrests had been prompted by the transcript of Saddam Hussein's initial interrogation as well as a briefcase of documents found in his hideout.
Time magazine, quoting a US intelligence official, reports that Saddam Hussein denied during initial questioning that his country possessed weapons of mass destruction.
"The US dreamed them up itself to have a reason to go to war with us," the magazine quoted the former president as saying.
A member of the Iraqi Governing Council (IGC) who met Saddam on Sunday following his arrest has said he seemed a demoralised man who swore profusely but showed absolutely no remorse.
"I found a very broken man...His body language showed that he was very miserable," Muwaffaq al-Rubaiye said.
Calls for trial
Iran has added its voice to calls for Saddam Hussein to be tried for crimes, saying he should be tried in an international court over the 1980-1988 Iran-Iraq war.
SADDAM: POSSIBLE CHARGES
Campaign against the Kurds in the 1980s, including the use of poison gas at Halabja
Suppression of Kurdish and Shia revolts after the first Gulf War
Brutality against the Marsh Arabs
Crimes committed during the wars against Iran and Kuwait
Possible involvement in recent attacks on coalition forces and other targets in Iraq
The US-appointed Iraqi Governing Council (IGC) has said he should be tried inside Iraq by Iraqi judges "under the supervision of international experts".
The current president of the IGC, Abdel Aziz al-Hakim, said Monday that Saddam Hussein could face the death penalty if convicted in an Iraqi court.
A special tribunal was set up in Iraq last week to try leading members of the former government.
Charles Heathley, spokesman for the US-led administration in Iraq, said on Monday he expected the new tribunal would charge Saddam Hussein "in due course" and ask the coalition to hand him over.
However, some human rights groups say an international tribunal - without the power to award the death penalty - would be preferable to a trial in Iraq.
The United Nations Secretary General, Kofi Annan, has said any trial of Saddam Hussein must be in a properly established court and must meet the basic standards of justice.
US officials say Saddam Hussein is being treated but not defined as a prisoner-of-war under the Geneva Convention.
The International Committee of the Red Cross (ICRC) has said it expects to have access to the captured former president .
There was no fixed time frame for the visit, a spokesman told AP.
"But we expect Saddam Hussein - as any other presumed, real or accepted PoW - will at some stage be visited by the ICRC."