A bomb exploded at 9am (0500 GMT) outside a bank in Kirkuk and killed 19 people, including pensioners and child street vendors selling groceries, police said.
Captain Salam Zangana, an official at a hospital where the victims were being taken, said another 53 people were wounded.
Kirkuk's police chief Major-General Torhan Abd al-Rahman told Aljazeera that 81 people were wounded.
The bomb was planted near a queue of people waiting outside the Rafidayn Bank in downtown Kirkuk, 290km north of Baghdad, police Colonel Shiraz Muhammad said.
Details of the bombing differed.
Muhammad said the blast was caused by a roadside bomb planted outside the bank and two cars parked nearby were set aflame.
The bomber exploded while
standing among Iraqis
But Abd al-Rahman told Aljazeera he thought a bomber detonated the bomb he was carrying while standing among Iraqis lined up in front of the bank.
Abd al-Rahman said: "Security is tight in Kirkuk city and in its suburbs," but he said he thought "terrorists" were still managing to target civilians.
"It is very obvious that they are killing a big number of civilians. This proves the terrorists' failure to reach police and army forces in Iraq," he said.
In Kanaan, 10 Iraqis, including two children, were killed and seven wounded by a car bomb, according to a toll provided by security and hospital sources.
"Ten people were killed in all and seven wounded," an Iraqi army officer said, adding casualties suffered by his soldiers to an earlier report of six dead and four wounded.
"The dead and wounded soldiers belonged to a unit called in as reinforcements in the town of Kanaan following a mortar attack against a police station.
"The soldiers were hit by the explosion of a car bomb that was parked nearby," the officer said.
"It is very obvious that they are killing a big number of civilians. This proves the terrorists' failure to reach police and army forces in Iraq"
Torhan Abd al-Rahman,
Kirkuk police chief
"Two policemen and four civilians, including two children below the age of 10, were killed and four civilians were wounded when the car exploded as a police patrol passed by," another police officer added.
A hospital director in Baquba said his teams had treated four people for wounds after they were brought in from the nearby town.
US soldiers killed
Two US soldiers were killed when a roadside bomb exploded next to their vehicle west of Baghdad, the military said on Tuesday.
The soldiers were killed on Monday near the city of Ramadi, 115 km west of Baghdad, it said in a statement.
Also on Tuesday, a doctor reported that the bodies of 13 Iraqi men, some beheaded, had been brought to a Baghdad hospital.
Dr Muhammad Jawad of western Baghdad's Yarmuk hospital said the bodies - either decapitated or shot in the head - were brought to the hospital late on Monday from near Khaldiya, a town 120km west of Baghdad.
Jawad said the bodies might belong to men who had been missing since their convoy that was delivering supplies to the US military was ambushed near Khaldiya on Thursday.
Two of the bodies were identified as an Iraqi police officer and an interpreter.
Vote of confidence
Al-Jaafari's cabinet was finalised
on 8 May
Meanwhile, Iraqi Prime Minister Ibrahim al-Jaafari on Tuesday obtained a vote of confidence in his government and its programme, a member of parliament said.
The 37-member cabinet was first put forward on 28 April and finalised on 8 May.
It obtained an "almost unanimous" vote of confidence from members of the 275-seat assembly present, said Shia MP Fattah al-Sheikh.
"The programme was debated by MPs who suggested certain modifications which were accepted and the vote followed and was almost unanimous," he said, without elaborating.
Al-Jaafari's government is set to be relatively short-lived, with general elections scheduled for 15 December once a new constitution has been put to a referendum.
Al-Zarqawi aide arrested
In other developments, the Iraqi government on Tuesday said it had arrested a senior aide to Abu Musab al-Zarqawi named Abu Ahmed Jasim al-Bazi.
The arrest was carried out on 7 June, an Iraqi government statement said. Al-Bazi was responsible for buying bombs, preparing booby-trapped cars and remote-control exploding devices used by al-Qaida in Iraq, it added.
A spokesman of the influential Association of Muslim scholars in Iraq (AMS) said an Iraqi-US force on Tuesday stormed the home of Shaikh Harith al-Dhari, AMS secretary-general in Khan Dhari district, west of Baghdad.
However, al-Dhari was not at home when the raid happened.