In one incident, up to 32 people were killed and 14 injured when a helicopter gunship attacked a school building which housed three displaced families in the militant-seized town of Alam, some 10 km northeast of Tikrit city, the official told Xinhua.
The three families are relatives of former Iraqi president Saddam Hussein, the official said.
Earlier, the families fled their homes in the village of Uoja, some 12 km south of Tikrit, after their place turned into a battlefield between the security forces and Sunni militant groups.
Meanwhile, two clashes erupted between security forces, backed by Shia militiamen and Sunni militant groups south of the city of Samarra, some 120 km north of Baghdad, the official added.
A total of nine Shia militiamen were killed and 34 injured during the two clashes, he said.
Salahudin province is a predominantly Sunni province and its capital Tikrit is the hometown of former president Saddam Hussein.
The security situation began to drastically deteriorate in Iraq since June 10 when violent clashes broke out between Iraqi security forces and hundreds of Sunni militants.