The attacks came a day after a spate of coordinated bombings in west Iraq killed 10 people, raising questions over the capabilities of Iraqi security forces with just months to go before all US forces must pull out.
Friday's violence in Tikrit, 160 kilometres (100 miles) north of Baghdad, also left 74 people wounded, including two members of Salaheddin provincial council, a senior policeman and a judge.
"We have received 19 dead bodies, and have treated 72 others who were wounded," Walid al-Duri, a doctor at the city's main hospital, said of the toll from the first blast as worshippers were leaving a mosque in central Tikrit on the main Muslim day of prayer at 12:45 pm (0945 GMT).
The bomb was hidden inside a fuel canister at the entrance to the mosque, where provincial officials often attend prayers.
A subsequent suicide attack inside the hospital where the victims were being treated killed two people and wounded two others, a security official in Tikrit said, speaking on condition of anonymity.
An interior ministry official in Baghdad put the toll from the first attack at 17 dead and 50 wounded, with six people were killed and 10 others wounded in the suicide bombing.