A suicide bomber killed 18 people and wounded 40 others when he rammed a fuel tanker into protective walls outside a police headquarters in Iraq's northern oil city of Baiji on Monday, police said.
In a separate attack south of Baghdad, police said eight people died and 31 were wounded when a suicide car bomber struck outside the governor's office in the Shi'ite city of Hilla.
Witnesses gave varying accounts of the Hilla attack. One said the bomber detonated his vehicle next to a fence of the governor's compound, while another said the blast happened at a checkpoint outside.
US and Iraqi officials blame most car bomb attacks in Iraq on Sunni Islamist Al-Qaeda.
There had been a relative lull in the number of such attacks in the past week since a car bomb killed 87 people at a Shi'ite mosque in central Baghdad on June 19.
Baiji police captain Ghazwan al-Janabi told Reuters the bomber rammed the fuel tanker into high protective walls near the back of the police headquarters in the city, 180 km (110 miles) north of the capital.
Janabi said police and prisoners kept in the facility were among the dead and wounded and that a large part of the building was destroyed.
Houses near the police building were also damaged and some of the casualties included residents living there, other police and hospital officials said. People were still being pulled from the rubble, said Khalid Ibrahim, a police officer at the scene.
Other police sources said police came under fire from unidentified gunmen while they were trying to secure the scene of the blast and assist the wounded.
US-led forces have launched simultaneous offensives in beltways and provinces around Baghdad to deny Al -Qaeda militants' sanctuary in farmlands and towns from where they launch car bomb attacks and other violence.
Tens of thousands of US and Iraqi troops are taking part in "Operation Phantom Thunder", one of the biggest offensives by US and Iraqi forces against Al- Qaeda in Iraq since the US- led invasion to topple Saddam Hussein in March 2003.
While attempting to put a lid on the violence, the offensives are also an attempt to buy time for Prime Minister Nuri al-Maliki's Shi'ite-led government to reach a political accommodation with disaffected minority Sunni Arabs.
The operations were launched after a security crackdown in Baghdad, which began in mid-February, squeezed militants out of the capital into surrounding areas.
US commanders say the combined operations were taking advantage of the completion of a build-up of US forces in Iraq to 156,000 soldiers. The additional troops have been sent to try to drag Iraq back from the brink of all-out sectarian civil war.