At least 36 Iraqi police officers have been killed and 70 wounded in a suicide attack on a police academy in Baghdad.
Violence also claimed lives in the Kurdish north on Tuesday
The policemen died when two attackers blew themselves up inside the academy at about 1245 (0945 GMT).
Hours later, a suicide bomber killed three people and injured 20 near a Baghdad cafe said popular with police.
The attack at the academy, claimed by al-Qaeda in Iraq, was the worst in Iraq since suicide bombers killed 74 people in two Shia mosques in November.
Initial reports suggested the bombers were both women but a claim published on the internet, and purporting to come from the al-Qaeda in Iraq group, said both were men.
The academy in eastern Baghdad is the capital's main police training centre and was the first of its kind to be opened.
That bombers could have penetrated what should have been a safe area raises further questions about the security of Iraqi police officers who, along with Iraqi troops, are a regular target of the insurgents, the BBC's Peter Grant reports from Baghdad.
As well as the Baghdad bombs, gun attacks were reported in Kirkuk in the Kurdish north, where at least three people were killed.
The first bomber reportedly detonated an explosive belt in or near a classroom.
As trainees and instructors tried to escape the scene there was a second explosion, apparently in a cafe inside the academy complex.
"We were sitting in the yard when we heard an explosion," police Maj Wisam al-Heyali said.
"Seconds later, we were hit by another explosion as we were running. I saw some of my colleagues falling down and I felt my hand hit but I kept on running."
Roads around the complex were sealed off and American forces helped the Iraqi emergency services to get the injured to hospital.
Officials said the early reports of women attackers were linked to the presence of two women visitors in the academy, whom police had been unable to search because there were no female officers available.
In its claim of responsibility, al-Qaeda accused the police of "shedding the blood and violating the honour of Sunni Muslims".
Tuesday's attacks come three days after 19 Iraqi soldiers were killed by militants near the city of Baquba, north of the Iraqi capital.
US and Iraqi officials have warned of an increase in attacks by insurgents in the run-up to the parliamentary elections next week.