All 32 were from the town of Ramadi in the insurgent heartland of Anbar province, which is fiercely opposed to the government.
One group of 17 were kidnapped and then shot dead after they signed up for the police force one week ago. They were found in the Baghdad district of the capital.
The other 15 were found bullet-riddled in two cars in Abu Ghraib, on the western edge of Baghdad.
US officials say the al-Qaeda leader in Iraq, Abu Musab al-Zarqawi, has been focusing on bombing and shooting Iraqi security forces, who are charged with eventually taking over security and enabling American troops to head home.
Sunni insurgents have also infiltrated Iraqi army and security forces in a bid to topple the government. However no one has claimed responsibility for the latest killings.
Meanwhile two car bombs near Baghdad's Mustansiriya University killed at least five people and wounded 25.
Another car bomb near the Health Ministry killed three people and wounded 25. Four other bombings in the city wounded at least 27 people.
Guerrillas attacked a police station near Saddam Hussein's hometown of Tikrit, killing four policemen. Rebels draw support from the Sunni minority once dominant under Saddam.
Maliki choosing cabinet
The violence continued as Jawad al-Maliki was working on choosing a cabinet, which will share power among Shi'ite Muslims, Sunni Arabs and Kurds to end a Sunni insurgency and sectarian violence.
Mr Maliki told CNN television healing the divisions wracking postwar Iraq was his biggest job as its first permanent premier.
"The main challenge that I see is the existence of a torn relationship in the Iraqi community with all the sectarian and ethnic backgrounds," said the tough-talking Shi'ite politician.
"So I have to work first on uniting all of these elements together and work on a national reconciliation on the basis of national dialogue and common interests."
Mr Maliki has four weeks to choose a new cabinet and form a government of national unity, widely seen as the only way to halt the sectarian violence.
The cabinet and Maliki's appointment, made by President Jalal Talabani on Saturday, must be ratified by parliament.
A key test of Maliki's ability to lead and to unite will be his choice of interior minister, perhaps the most sensitive post given the brutal past many Iraqis endured under Saddam's rule and a present racked by relentless instability and violence.
Iran rejects talks
With Mr Maliki in the process of forming a coalition and ending four months of political paralysis, Shi'ite neighbour Iran said there was no longer any need for talks with the US to discuss Iraq's problems.
"By God's will, we think that right now, because of the presence of a permanent government of Iraq, there is no need," President Mahmoud Ahmadinejad told reporters in Teheran.
During the impasse among Iraqi leaders over the shape of a new government that followed December elections, Iran and the US had agreed to discuss how to stabilise Iraq.
In Baghdad's heavily fortified so-called Green Zone, the court trying Saddam for crimes against humanity heard that signatures of the former leader and six co-accused on documents linking them to the killing of 148 Shi'ites in the 1980s were genuine.
The prosecution had demanded the court commission a team of criminal experts to authenticate signatures and handwriting of the defendants.
Saddam and his half brother, Barzan al-Tikriti, have refused to give samples of their writing but both have said there was no crime in prosecuting the 148 from the village of Dujail because they were accused of trying to kill the former Iraqi president.
The defendants could face death by hanging if found guilty.