The bloodshed on Wednesday came as a 1000-strong US force backed by aircraft battled fighters in the west of the country in an operation that the military said had killed up to 100.
A car bomb killed 38, mostly civilians, and wounded 84 in a busy market area of Tikrit, near the hometown of ousted Iraqi president Saddam Hussein, about 180km north of Baghdad.
In Hawijah, northeast of Tikrit, a bomber wearing a belt of explosives struck outside an army recruitment centre, killing 35 and wounding 33, the army and medical sources said.
The Ansar al-Sunna group linked to al-Qaida claimed the bomb attacks in statements posted on its website.
"Your brothers planted a car bomb in a Tikrit public square used by dozens of apostates working on the local US base, and exploded it," said a message, attributed to the group, referring to Iraqi security forces.
Another Internet statement whose authenticity also could not be verified said "a hero of Islam, Abu Abd Allah al-Turkmani, blew himself up among a group of apostates of the Iraqi national guard at a recruitment centre in Hawijah".
Meanwhile, in Baghdad, at least three people were killed and 10 wounded in two separate explosions, one of them outside the Dura police station in the south of the city, police said.
Seven other Iraqis were killed in attacks across the country.
Survivors of the Hawijah bombing
were treated in a nearby hospital
Two Iraqi soldiers were killed and five others were wounded in an afternoon attack on their convoy in western Baghdad, a Ministry of Interior source said.
Elsewhere, a police captain was killed by four armed assailants in Baquba, 60km northeast of Baghdad, said police Lieutenant-Colonel Kassem Muhammad.
And a man blew himself up as he tried to sabotage an oil pipeline, said Lieutenant-Colonel Saad Mahmud, near the oil city of Kirkuk, about 250km north of Baghdad.
In Basra, a bomb planted near a pipeline that supplies gasoline to a large Iraqi fertilizer plant exploded, killing one employee, wounding more than 20 and starting a fire that heavily damaged the factory, police and a security guard said.
Black smoke billowed for hours from the South Fertilizers plant before firefighters managed to put out the blaze, which destroyed about 60% of the plant, police said.
About 60% of the Basra plant
The plant was considered one of the largest fertilizer factories in the Middle East.
Anti-US fighters have stepped up attacks this month since Prime Minister Ibrahim Jaafari formed Iraq's first elected government in more than half a century.
Since the beginning of May, more than 400 people have been killed in car bombings and other attacks.