Meanwhile, a civilian plane was hit by a missile as it took off from Baghdad International Airport - it managed to land safely - and a leading Shia cleric narrowly missed being killed by a dud rocket.
A four-year-old girl was among three civilians and six police officers killed in the small town of Khan Bani Saad, 20km (12 miles) from Baghdad, when a bomber rammed a vehicle packed with explosives into the police station, according to an "initial" toll from the US military.
Minutes later another suicide assailant blew himself up outside the police station in the provincial capital of Baquba further north, killing seven Iraqi police and two civilians, said Colonel Bill MacDonald, spokesman for the US Fourth Infantry Division, which patrols the region.
A further five Iraqi police were still missing from that attack, MacDonald said.
The horror of the human detritus from the two attacks was so great that doctors said it was difficult to be precise about the toll.
"We received so many body parts it's difficult to know how many died," said doctor Talib Husayn al-Tamimi. "We've been utterly overwhelmed."
A further 10 people were wounded in the 7:30 am (0430 GMT) attack in Khan Bani Saad which tore a massive hole through the wall of the police station.
A nurse carries a wounded boy
injured in Khan Bani Saad attack
"The Chevrolet car came very fast ... Police opened fire but it didn't stop," police chief Ismail Kanu al-Askari told AFP.
In the Baquba bombing, another 20 people were wounded, according to the US toll.
"I had just arrived at work when I saw the car charging the station," said Lieutenant Imad Kazim Rahim. "Police opened fire and the car exploded before it could hit the building."
The northeastern province of Diyala, where the two towns are located, has long been a hotbed of anti-occupation insurgency but the twin attacks were the most devastating here to date.
They follow a spate of suicide bombings across Iraq from the capital, to the central Shia Muslim pilgrimage city of Najaf and the northern oil centre of Kirkuk.
Plane hit by missile
A civilian plane belonging to international express courier DHL was hit by a SAM-7 surface-to-air missile over Baghdad on Saturday forcing it to make an emergency landing, the US military said.
"It caught fire, it turned around and came back to the airport where it safely landed. The fire was taken out. There are no injuries," a US military official said.
It was the first time a civilian aircraft has been fired on as it used Baghdad airport.
It was the first time a civilian aircraft has been fired on as it used Baghdad airport. Eight official or military aircraft have been targeted as they have flown in or out of Baghdad, according to Iraqi transport ministry figures.
Guerrilla attacks have brought down five US Army helicopters in Iraq over the past month, killing 39 people.
Shia cleric escapes
A leading member of Iraq's US-appointed Governing Council, Shia leader Abd al-Aziz al-Hakim, also had a near miss in a Baghdad mosque on Friday, his son said on Saturday.
Muhsin al-Hakim said that attackers fired a Russian-made rocket from gardens near the mosque but it failed to explode. The missile missed its target and wrecked a car parked 100 metres away. No one was injured.
"It was a terrorist attack on his life by remains of Saddam's regime and those who want instability in Iraq. They are pursuing the same goals as those who killed Muhammad Baqir al-Hakim," Muhsin al-Hakim told Reuters in Tehran.
The attack took place on the same day that guerrillas fired Russian-made Katyusha rockets from donkey carts at Iraq's Oil Ministry and two Baghdad hotels used by Westerners.