Ten people were killed in a car bombing near one of Baghdad's main bus stations.
The bomb, which also injured 18 people, went off in a crowded market place near al-Nahda bus station in the city centre on Friday, a defence ministry official said.
Another car bomb in central Baghdad killed at least nine people and wounding 31.
Elsewhere in the capital, a bomb went off in the southern neighbourhood of al-Bayaa wounding 18, and there were two blasts in an upscale west Baghdad neighbourhood that wounded five. No further details of the attacks are available.
The blasts came after Nuri al-Maliki, the Iraqi prime minister, declared security in Baghdad to be the new government's top priority.
In western Baghdad, police said three bodies were found with bullet wounds and signs of torture.
Basra imam killed
Meanwhile, in the predominantly Shia southern city of Basra, a Sunni imam and a bodyguard were killed by assailants in a drive-by shooting as they travelled to their mosque for Friday congregational prayers, police said.
Sunni leaders have closed 170 mosques in the southern city of Basra in protest against the killing of Wafiq al-Hamdani, the imam.
Sunni leaders have closed 170
mosques in Basra in protest
The Sunni Waqf (Endowments) Centre said the closure is in protest at "the offensive displacement campaign and assassinations against Sunnis in the modern age".
The leaders called on the Arab countries to play a role in "saving whatever can be saved".
They also called on the Iraqi government to use all means necessary to return security to the city, Aljazeera said
In the northern city of Kirkuk, a roadside bomb detonated near a police patrol in the south of the city, killing one policeman and wounding four.
Also in Kirkuk on Friday, armed men shot dead a police officer and his friend as they were having tea outside his house, police and hospital sources said. Another friend was wounded in the drive-by shooting.
Other Iraqi cities and towns in the news for violence were:
Kut - Police said four bodies were found on Friday in Kut, 160km southeast of Baghdad, including the tortured corpse of a member of the Shia Mahdi Army militia. Police also discovered two beheaded bodies in Kut.
Suwayra - Police said they found on Friday near Suwayra, south of Baghdad, the body of a member of the Mahdi Army militia which had bullet wounds and showed signs of torture.
Baghdad - Assailants killed the coach of Iraq's national tennis team and two of his players while they were driving through Baghdad on Tuesday, ministry of interior and police sources said on Friday.
Baquba - Employees abducted from the local Diyala Television station in Baquba, 65km north of Baghdad, watched armed men execute two policemen held with them before being released, one of the hostages said.
Muqdadiya - Armed men stormed a wedding party on Thursday and abducted the groom, his uncle and cousin and a guest at the party. All were found the next day, beheaded near Muqdadiya, 90km northeast of Baghdad, police said on Friday.
In a separate incident, the speaker of Iraq's national assembly condemned what he said was the arrest of the brother of a member of parliament by US and Iraqi forces in a raid on her house on Friday.
Mahmoud al-Mashhadani said in a statement that US and Iraqi forces arrested the brother of Sunni Arab parliamentarian Taysir Awwad at her home.
"I condemn the arrest which violates the immunity of the house because she is a member of parliament," he said.
The US military had no immediate comment.