There has been an explosion at a shrine in the holy city of Karbala south of the Iraqi capital Baghdad.
Karbala has seen outbreaks of violence before
Unconfirmed reports say three people have been killed and 12 injured.
The US military says that one American soldier was killed by a homemade bomb in the northern town of Tikrit.
And explosions and mortar fire were also heard near the US headquarters in Baghdad.
One mortar struck a camp of the 2nd Armoured Cavalry Regiment but caused no injuries, a US military statement said.
Two others hit unspecified locations in central Baghdad but there was no damage to buildings of the US-led occupation, the military said.
The Tikrit attack left one US soldier dead and a second wounded, according to an American military spokesman quoted by Reuters news agency.
The blast was caused by an "improvised explosive device", the spokesman said.
Over 130 American soldiers have died since President Bush declared the war over on 1 May.
In Karbala, the blast on a busy street happened close to the gold-domed Imam Hussein shrine - one of the holiest sites in Shia Islam.
There are conflicting reports on the cause of the blast.
Mohammed Abu Jaffar al-Assadi, a Shia cleric who arrived
at the scene minutes after the blast, said a bomb had apparently been planted in a
But other witnesses said it might have been concealed in a bag left outside a hotel.
All the dead and injured apparently were passers-by.
Karbala was rocked last month by clashes between supporters of rival Shia factions. Also in October, gun battles broke out between US troops and backers of a maverick Shia preacher, leaving three American soldiers dead.
Judge reported killed
A senior judge in Najaf has been shot dead, apparently by militants opposed to his involvement in US-backed judicial commission probing former officials in the Saddam Hussein regime, the AFP news agency reports.
Muhan Jabr al-Shuwaili was driven out of the city early on Monday and murdered, according to Najaf's prosecutor general, Aref Aziz, who was also abducted but then released.
Al-Shuwaili had supported the Baath Investigative Commission, set up in August to act on complaints against former Saddam loyalists.