Iraqi militants have ambushed a US convoy and demonstrations in support of Saddam Hussein in some flashpoint towns near Baghdad have turned violent.
Three soldiers were wounded by a roadside bomb in Tikrit
The US army says it killed at least 11 militants who ambushed the convoy in the northern town of Samarra on Monday.
No Americans were injured in the battle
100 km (62 miles) from Baghdad.
The violence came amid debate about how to try the captured former Iraqi leader, with both the Iraqi Governing Council and the UN weighing in.
Reports suggested that the Council was considering trying Saddam Hussein as early as next year - much sooner than US officials have been anticipating.
A senior US official said a decision on how the former Iraqi leader might be prosecuted had to be taken first, and a mountain of evidence sifted through.
In New York, the United Nations Security Council is meeting on Tuesday to discuss future plans for Iraq.
Members will also examine the accelerated timetable for handing over power to a transitional government in June.
The dramatic capture of Saddam Hussein announced on Sunday has not quelled anti-US resistance in Iraq.
Supporters of Saddam Hussein clashed with US troops in towns in the Sunni Muslim belt and at least three gunmen were killed in Falluja and Ramadi.
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
On Tuesday, three US soldiers were wounded when their military vehicle was hit by a roadside bomb in Tikrit.
Independent reports of the fighting in Samarra - scene of a bloody battle at the end of November - were not immediately available on Tuesday.
The US army blamed the "complex" ambush on Saddam loyalists.
Monday evening saw violent protests across the Sunni Muslim belt, the heartland of the ousted Baathist regime:
- Up to 1,000 students demonstrated against the "humiliating" capture of Saddam Hussein at the university in Mosul;
- In Falluja, hundreds of residents rioted, seizing the offices of the US-appointed mayor, witnesses told Reuters news agency. In the confusion, gunmen opened fire at US troops and wounded one, the US military said. One gunman was killed and at least two wounded in return fire;
A gun battle also erupted in Ramadi, where about 750 people attended a pro-Saddam rally.
One US soldier was wounded while the Americans said they had shot dead two gunmen and wounded two;
And in Tikrit, about 700 people demonstrated in the city centre, chanting "Saddam is in our hearts, Saddam is in our blood" as US soldiers and Iraqi policemen yelled back "Saddam is in our jail", AP news agency reports.
Protesters clutched old photographs of the captured former president or pasted posters of him up on walls.
The angry rallies contrasted with scenes of jubilation in Baghdad and in the largely Shia Muslim south of Iraq at Saddam Hussein's capture.
UN Secretary General Kofi Annan has called for a fair and open trial for Saddam Hussein, and said that the UN remained opposed to the death penalty.
Security Council members are to examine the accelerated timetable, drawn up by the US coalition and the US-appointed Iraqi Governing Council, on handing over power to a transitional government next June.
Saddam Hussein is now being held for interrogation at an undisclosed location, but the International Committee of the Red Cross says it hopes the US military will allow a visit so that it can check on his conditions.
The US says that Saddam Hussein is being treated according to the Geneva Convention, but has not yet confirmed that he is considered a prisoner of war.
A member of the IGC who met Saddam Hussein 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.
The IGC has said the former leader should be tried inside Iraq by Iraqi judges "under the supervision of international experts".
Mr Rubaiye said punishment could be swift, after the IGC takes over the sovereignty of Iraq at the end of June next year.