Sunni insurgents may also be responsible for the attacks in Dora, hoping that the bombings will spark a sectarian backlash. But Shiite militias remobilizing and sending fighters to confront mostly Sunni rebels in neighboring Syria also could be to blame.
Earlier in the day, police said gunmen killed two soldiers in an assault on their security checkpoint in the restive city of Mosul, 360 kilometers (225 miles) northwest of Baghdad.
Hours later, a roadside bomb killed a municipal council member and his son in a town near Mosul. Gunmen in another area just south of Mosul also sprayed a security checkpoint with bullets, killing two policemen.
Hospital officials confirmed those casualty tolls. Officials spoke on condition of anonymity because they weren't authorized to release the information to reporters.
Also on Sunday, a spokesman for Iraq's prime minister said that outgoing Iranian President Mahmoud Ahmadinejad plans to visit Iraq later this week. It will be the Iranian leader's second visit to neighboring Iraq while in office.
Iraq's Shiite-led government has strengthened ties with Tehran since the toppling of dictator Saddam Hussein in 2003. The closeness rankles Sunnis. Many in their ranks believe Baghdad is too friendly with the Shiite powerhouse, the main regional backer of Syria's embattled President Bashar Assad.
Iraqi Prime Minister Nouri al-Maliki's spokesman, Ali al-Moussawi, said Ahmadinejad plans to arrive for a visit to Iraq on Thursday. He said Ahmadinejad would meet with senior Iraqi officials and visit Shiite holy shrines in Najaf and Karbala during the two-day visit.
Ahmadinejad, who leaves office in August, visited Iraq for the first time in March 2008.
Associated Press writer Nabil al-Jurani in Basra, Iraq, contributed.
Adam Schreck can be reached at www.twitter.com/adamschreck