The dead included 20 Iraqi troops, a US soldier and a British soldier.
The American soldier was killed in the Anbar province of Baghdad.
The British soldier was fatally wounded in a mortar attack on a British base in Basra.
The deadliest attack on Tuesday occurred when a roadside bomb struck a bus carrying Iraqi soldiers near Beiji, 240kilometres north of Baghdad. All 24 people on board were killed. Police said that all but four of the dead were Iraqi soldiers.
In Baghdad 14 people died and 37 were wounded when a car bomb exploded at a bank where police and soldiers were collecting their monthly paychecks.
The blast set several other cars ablaze and scattered dismembered bodies along the street as bystanders carried the injured to ambulances.
It was the third attack in less than a week in Karradah, a mostly Shia neighbourhood in central Baghdad that is home to several prominent politicians.
A car bomb killed seven people - six of them civilians - in Muqdadiyah, about 100kilometres northeast of Baghdad.
In another attack, gunmen ambushed a minibus carrying employees of a power station to their homes in the Shia district of Sadr City, killing five passengers and wounding six.
US troops arrested a Baghdad-area representative of the Shia cleric Muqtada al-Sadr, who leads the Mahdi Army group on Tuesday.
The arrest of Sheikh Ahmed al-Ashmani was reported by al-Sadr's staff, who said that 10 other members of the movement were also detained.
There was no confirmation from the US army.