Sunday's discoveries came on a day when drive-by shootings and bombings killed at least eight Iraqis, including a senior Industry Ministry official and a top Shia cleric.
The attacks came as US Secretary of State Condoleezza Rice made a heavily guarded surprise visit to Iraq to meet leaders of the new national government and urge patience for Iraqis weary of repeated bombings and insecurity.
US marines said a seven-day offensive near the Syrian border against supporters of Jordanian-born Abu Musab al-Zarqawi ended late on Saturday, killing more than 125 fighters, wounding many others and detaining 39 said to be of intelligence value.
The offensive came amid a surge of attacks that have killed more than 450 people in more than two weeks since Iraq's first democratically elected government was announced.
Series of attacks
Armed men continued to launch attacks on Sunday in a seemingly endless campaign apparently aimed at enflaming sectarian tensions, destabilising Iraq's new government and forcing US-led troops out of the country.
Armed men in two cars shot dead Industry Ministry official Colonel Jassam Muhammad al-Lahibi and his driver in western Baghdad's Ghazaliya neighbourhood, police and Interior Ministry officials said.
A leading Shia cleric, Shaikh Qasim al-Gharawi, and his nephew were shot dead in another drive-by shooting, this time in the capital's New Baghdad neighbourhood.
"The insurgency is very violent, but you can beat insurgencies not just militarily. You can beat them having a political alternative that is strong and in which all Iraqis are invested"
US Secretary of State
Al-Gharawi was an aide to Iraq's top Shia cleric, Grand Ayat Allah Ali al-Sistani, and responsible for conveying al-Sistani's edicts to Shias in parts of Baghdad.
Three groups of men, most bound and blindfolded, were found shot in the head in Baghdad and locations south and west of the capital.
Police in eastern Baghdad's impoverished Sadr City discovered 13 slain men, most appearing to be aged in their 20s and three heavily bearded, lying face down in a shallow grave in a rubbish-covered lot.
Residents said they saw people in a truck dump the bodies on to the ground early on Sunday and cover them with soil.
Judging by the nature of the wounds and the condition of the bodies, police officials thought the men were shot either late on Saturday or early on Sunday.
Police made a similar discovery late on Saturday in Huqul, a town in the Latifiya area, about 40km south of the capital.
More than 450 people have been
killed in the past two weeks
The bodies of 11 men with their hands tied behind their backs and bullet wounds to the head were found dumped in a deserted chicken farm.
Latifiya is in an anti-US stronghold that has become known as Iraq's Triangle of Death. The region has been the scene of repeated tit-for-tat killings and kidnappings between Shia and Sunni Muslim groups.
In the battleground city of Ramadi, 115km west of Baghdad, the slain bodies of 10 Iraqi soldiers were found on Saturday, an Interior Ministry statement said.
The men were shot and their bodies dumped in eastern Ramadi's Abu Obaid area, the statement added without providing further details.
An Iraqi military expert told Aljazeera on Sunday that the wave of violence in Iraq is rooted both in opposition to the US-led reconstruction and sectarian divisions.
Retired brigadier general Muhammad al-Askari said much of the violence against police and Iraqi national guardsmen was led by what he called the Jihad and the Tawhid groups, which see government forces as allied to US-led troops.
But he said sectarian tensions were likely to worsen if the country's instability continued.
"All possibilities are likely as the security situation worsens. Each party tends to throw accusations against the others," Askari said.
Downtown Baquba's two explosions - detonated about five minutes apart in a busy street as residents were heading to work - killed four Iraqis and wounded 37, police and hospital officials said.
The first, a car bomb, targeted the convoy of Diyala provincial Governor Raid Rashid Hamid al-Mullah Jawad, who escaped unharmed. Three of Jawad's guards were wounded.
Minutes later, a bomber dressed as a police lieutenant blew himself up when a police major stopped him from entering a court building about 500m away. Three police officers were killed in the blast, and three other officers were injured.
About 20 minutes later, seven mortar rounds slammed into a downtown Baquba residential area near al-Rahma Hospital, badly damaging five homes and injuring three men and one woman. Those who fired the mortars were not found.
US forces say they are pursuing
al-Zarqawi supporters in Iraq
"Yes, the insurgency is very violent, but you can beat insurgencies not just militarily," Rice told reporters in Iraq. "You can beat them having a political alternative that is strong and in which all Iraqis are invested," Rice said.
The one-day trip was her first visit to Iraq as the United State's top diplomat. Her first stop was the town of Salah al-Din in Kurdish northern Iraq, where she met Kurdish Democratic Party leader Masud Barzani.
In Baghdad she had a full schedule of meetings planned with top government officials, including Prime Minister Ibrahim al-Jaafari, cabinet members and a group of deputy prime ministers.