The Baghdad blast went off in the eastern district of Jadida, and mangled several market stalls and scattered wreckage across the area.
In Kirkuk, one of the explosions appeared to target a Shi’ite mosque in the city’s central area of Mousala, killing two and wounding two.
Police said earlier this morning, explosives experts were called to the north-eastern entrance of the city after residents spotted a roadside bomb.
As the experts dismantled it, a car bomb parked nearby exploded, wounding two of them and destroying a nearby police car and a vehicle owned by a local resident.
Earlier, an army general was killed in Baghdad, shot dead by unidentified gunmen as he drove to work, and a police colonel was shot dead an hour later as he left his home in the city’s south.
Staff General Iyad Imad Mehdi was seriously wounded by gunmen at 07.15 am (1315 AEST) on leaving his home in the western Jihad district,” said an Interior Ministry official.
“He died at Yarmuk hospital,” the official said, adding that the gunmen had escaped in a car.
One hour later, police Colonel Jamal Ahmed Hussein, who worked at the Interior Ministry, was gunned down on leaving his home in the al-Amin district, in the southeast of the capital, the official said.
“He was shot several times and taken to Kindi hospital where he died,” the official added.
Meanwhile, two US marines were killed when their armoured vehicle drove over a mine in northwest Iraq during an offensive against insurgents.
The US military said 14 others were injured.
US troops are involved in a major operation in the country’s west to flush out supporters of rebel leader Abu Mussab al-Zarqawi.
The latest violence comes a day after at least 76 people were killed and over 120 wounded in a bloody wave of bomb blasts in three Iraq towns.
Five morning explosions on Wednesday hit Tikrit and Hawijah in the north, as well as in Baghdad.