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 just before all US forces must pull out.
Yesterday's violence in Tikrit, 160 kilometres north of Baghdad, also 75 wounded people including two members of Salaheddin provincial council, a senior policeman and a judge.
"The first attack killed 19 people and we treated 72 wounded," said a doctor at Tikrit hospital, speaking on condition of anonymity.
A suicide bomb attack on the hospital, timed to coincide with an MP's visit with the victims, killed a further five and wounded three, he said, adding the lawmaker was unscathed but two of his bodyguards were among the dead.
A provincial security official, who also did not want to be named, confirmed both tolls. An interior ministry official in Baghdad said 23 people were killed and 60 wounded in the two attacks.
The first bomb, hidden inside a fuel canister, detonated as worshippers were leaving the mosque in the tightly secured area of central Tikrit that is home to provincial government offices on the main Muslim day of prayer at around 0945 GMT.
The suicide attack occurred about eight hours later in the evening, as lawmaker Mutasher al-Samarrai visited victims at the hospital.
Yesterday's violence was the worst in Tikrit since a March 29 Al-Qaeda raid on the city's provincial council offices, which led to a bloody hours-long gun battle with security forces that left 58 people dead.
Tikrit was the hometown of now executed dictator Saddam Hussein and is the capital of mainly Sunni Arab Salaheddin province, which was a key battleground in the insurgency that followed the US-led invasion of 2003.
On Thursday, at least three explosions killed 10 people in the western city of Ramadi.
The two days of violence raise questions over the ability of Iraqi forces to secure the country, with 45,000 American troops due to withdraw at the end of the year under the terms of a bilateral security pact.
Violence in Iraq is down from its peak in 2006 and 2007, but attacks remain common. A total of 177 people died in May as a result of violence, according to official figures.