Twenty-two Iraqis were killed and 58 wounded when a car bomb exploded in a crowded popular market place at sunset in Husseiniya, just northeast of the capital.
As police and rescue workers swarmed through the area, a second bomb was discovered and defused.
Only an hour earlier, 12 people were killed and 32 wounded when a car bomb, ripped through a used car lot in Hillah, the capital of Babel province, south of the capital.
And after dark, nine people died and another 10 were wounded when a bomb exploded as they queued outside a Baghdad bakery to buy bread.
The blasts came as Prime Minister Nuri al-Maliki told BBC he would fill his government's contentious security posts by the end of the week.
Mr Maliki also said he had a better chance of tackling the daily carnage in Iraq than his predecessors because he was head of the country's first full-term administration since the US-led invasion.
"We took a long time because it is an important task that means a lot to Iraq, Iraqis and to the political process," Mr Maliki said, as 10 days after the rest of the government was formed.
Rocket attack
Baghdad's interior ministry was targeted when a rocket slammed into its third floor, killing two female employees and wounding four policemen.
A station wagon had been fitted with improvised launchers and set to go off with a timer in the neighbourhood of Zayuna, near the ministry, but exploded after the first rocket was launched.
Four mechanics leaving an industrial area in Bayaa, also in south Baghdad, were killed by gunmen and four other people died in various incidents around the capital.
Meanwhile the Pentagon has announced that 1,500 troops from an armoured brigade in Kuwait are to be sent to western Iraq's Anbar province to reinforce those combating a surge of violence from Al-Qaeda.
The reinforcements come amid renewed clashes in the flashpoint Anbar cities of Fallujah and Ramadi. A wave of assassinations of local Sunni tribal leaders has decreased their co-operation with US forces.
Efforts to involve local tribes in providing security in the province have foundered in the past few months in the face of a campaign of intimidation and murder by insurgents.
On Sunday, pro-US tribal leader Osama Jedaan, whose Karabla tribe is based near Iraq's border with Syria, was assassinated.
A key part of the coalition strategy for Iraq is the eventual handover of security duties to Iraqi security forces, something Prime Minister Nuri al-Maliki has predicted could take place near the end of 2007.
The process is being hindered by the lack of a defence minister, who is expected to be a Sunni Arab, but the appointment has to be acceptable to the diverse political and sectarian groups in the government of national unity.
Diplomat freed
In other developments the captors of a United Arab Emirates diplomat held in Iraq for a fortnight have freed their hostage.
The Emirati foreign minister confirmed that Emirati diplomat, Naji al-Nuaimi, who was kidnapped in Iraq on May 16, was released on Tuesday in good health
"The Emirates thank the Iraqi government and appreciates the efforts that the government went to... to ensure the Emirati diplomat's safety and secure his freedom,” said Abdallah Ben Zayed al-Nahyane.
"The Emirates thank all the Iraqi political forces for the role they played in the liberation of Naji al-Nuaimi," he said.
And a leading insurgent commander Ahmed Hussein Dabash Thamer al-Batawi, suspected of involvement in the beheading of hundreds of Iraqis, has been captured in Baghdad, Mr Maliki's office said.