The battle for Tikrit, the hometown of Saddam Hussein, is a key test for the Iraqi forces.
The two officials say security forces entered Alam this morning and hours later gained full control of the town. The two spoke on condition of anonymity since they are not authorized to talk to reporters.
Ahmed al-Karim, the Salaheddin provincial council chief, says progress had been slow due to roadside bombs and sniper attacks.
Iraqi forces launched the large-scale mission last week to retake Tikrit, held by the Islamic State militants since June.