Aljazeera said police stations and a checkpoint south of the city were attacked by fighters at about 7.30am (0430 GMT).
"They attacked with heavy weapons," Major Ali al-Tikriti said. "It was not clear if the attackers suffered any casualties."
Arkan Muhammad, a government official in Tikrit, said 12 men were killed when the police station was hit. The station is about 20km south of the city, ousted president Saddam Hussein's hometown.
US military spokesman Captain Bill Coppernoll confirmed that there had been an attack on police near Tikrit, but could not provide casualty figures.
Iraqi journalist in Tikrit Muhammad al-Badri, told Aljazeera Tuesday was a bloody day for Iraqi police in Tikrit, as armed men launched numerous attacks targeting police stations.
He added that the first and most violent attack targeted Dijla police station, 25km south of Tikrit city.
The attackers stormed the centre and killed 12 policemen, then blew up the station.
|Tikrit suffered a high death toll|
Al-Badri added that the second attack targeted an Iraqi police checkpoint south of the city, killing a captain and injuring two policemen.
The third attack targeted al-Ishaqi area, 85km north of Baghdad.
A huge number of fighters attacked al-Ishaqi police station, the emergency squad and the al-Ishaqi directorate building, killing four Iraqi policemen and injuring two others, police sources told the Iraqi journalist.
He said the attacks seemed well organised and coordinated.
No one has yet claimed responsibility for the attack.
Master Sergeant Robert Powell, of the Tikrit-based US 1st Infantry Division, also confirmed that various police checkpoints around Tikrit had been attacked in at least four separate incidents.
Baghdad car bomb
In a separate incident in Baghdad, a car bomb targeting the chief of staff of the US-backed Iraqi National Guard killed one person and injured eight, witnesses and a police source said.
The Baghdad car bomb missed
its target, but killed one person
General Mudhir al-Mula, who was leaving his home on the edge of the Adhamiya district in a convoy when the bomb went off, apparently escaped unhurt.
Al-Mula, a Shia Muslim, was also a general under Saddam's rule.
Witnesses said the car laden with explosives appeared to have been parked close to the general's house in a long line of vehicles waiting overnight for petrol, a common feature of Baghdad's fuel crisis.
Baquba police toll
Meanwhile, six Iraqi national guardsmen were killed and another 18 were wounded northeast of Baghdad, according to a doctor at Baquba's main hospital.
A witness, Muhammad Ali Khalid, said a morning patrol was hit first at around 07:30 GMT.
Backup was sent to the scene, and as guardsmen were busy diffusing another suspected roadside bomb, a second car bomber sped into their midst and blew his
At least 25 other policemen and guardsmen were killed in other attacks Tuesday around the town of Samarra north of the capital.