A roadside bomb hit a bus carrying soldiers between the towns of Tikrit and Baiji, north of Baghdad on Tuesday. At least 24 people were killed including many soldiers, a military source said.
A curfew was imposed in Baiji after the blast.
In Baghdad, a car bombing in the Karradah neighbourhood killed at least 14 people and wounded dozens more.
The parked car exploded near a bank where Iraqi security forces get their wages on the first of every month. Several soldiers were reportedly killed in the blast.
Sectarian fighting between Shias and Sunnis in Karradah has been increasing in recent months. Last Thursday, rockets and mortars struck the area, destroying buildings and killing at least 31 people. A car bomb exploded at the same time.
Karradah is one of the few areas of the country entirely under the control of Iraqi security forces.
Sectarian violence is rising in
Another car bomb exploded near a police patrol in Muqdadiyah in the Diyala province of northern Iraq. Seven people were killed and at least eight injured. The explosion happened as the police patrol drove by, an official of a joint Iraqi-US security force centre said.
In the northern city of Kirkuk, a roadside bomb killed two police and wounded a third while they were on patrol.
Another roadside bomb narrowly missed a car belonging to the ministry of electricity, killing one civilian and wounding another in Zayouna in eastern Baghdad, police said.
A British soldier has died after a mortar attack on a base in the southern Iraqi city of Basra, Britain's defence ministry said.
The soldier, attached to the 1st Battalion Light Infantry, died after being airlifted from a base in Basra to a field hospital at Shaibah Logistics Base, on the outskirts of the city.