Thirteen of the corpses were found in Baghdad's Sadr City.
Police Lieutenant Colonel Shakir Wadi Al-Maliki said the 13 slain men, most appearing to be aged in their early 20s, were wearing civilian clothes and lying in a shallow grave in a vacant lot.
Judging by the nature of their wounds and the state of bodily decomposition, police officials believed the men were shot either late on Saturday or early on Sunday.
An Associated Press photographer saw the bodies lying in the grave with their hands tied behind their back, eyes blindfolded and at least three bullet wounds in each of their heads.
Eleven corpses of men shot dead were also discovered by police in the town of Iskandariyah, south of Baghdad, police and medical sources said.
"Police found 11 bodies in an agricultural zone close to Iskandariyah. All are of middle-aged men," police captain Yahya al-Mamudi told AFP.
"We have received 11 bodies. They were shot dead a few days ago," said Mohammed al-Saidi of the hospital in Iskandariyah.
Police said at least three of the dead had been identified as Iraqi soldiers.
The defence ministry, in the meantime, said 10 bodies of soldiers, all with their throats cut, had been discovered close to the town of Ramadi, west of Baghdad.
A ministry statement said the soldiers had been killed on Thursday.
These grisly finds come on a day that saw two separate drive-by shootings in Baghdad that killed a senior Industry Ministry official, his driver and a Shia cleric.
Two car loads of men opened fire on an Industry Ministry official and his driver, killing both in a hail of bullets, police Major Musa Abd al-Karim said.
The victims were travelling through Baghdad's al-Gazaliya area when they were attacked, Abd al-Karim said.
An Interior Ministry official identified one of the victims as Colonel Jasim Muhammad al-Lahibi, a former intelligence officer who worked as an assistant director in charge of government-owned buildings.
In the other incident, attackers killed Shia cleric Shaikh Qasim al-Gharawi and his nephew at about 9am in the capital's New Baghdad neighbourhood, police Lieutenant Colonel Ahmad Abud said.
Bid on governor
Meanwhile, Diyala province's Governor Raid Rashid Hamid al-Mullah Jawad survived a bomb attack in Baqouba.
Ambulances attended the scene
where body parts lay scattered
A hospital official said four people were killed in the attack and 37 others injured.
The attack, on Sunday, began when a bomber blew up his vehicle in the path of the governor's convoy.
Police said nobody was wounded in the first blast, but a second bomber ran towards the convoy on foot and detonated an explosives belt, killing four people.
The two explosions were detonated about five minutes apart in a busy street in downtown Baqouba, 60km from Baghdad.
Ambulances attended the scene where body parts, including a hand and foot, lay on the ground amid pools of blood and shards of glass.
Raid Abd al-Munim, head of Baqouba General Hospital, said the bodies of four people killed in the blasts were brought to his hospital, along with 37 others suffering various injuries.