Other violence in the country left one U.S. soldier and two Iraqi policemen dead, while Iraq's planning minister escaped an assassination attempt.
Authorities found 26 of the corpses on Tuesday in a field near Rumana, a village about 12 miles east of the western city of Qaim, along the Syrian border, said police Capt. Muzahim al-Karbouli.
Each body had been riddled with bullets, apparently several days earlier. They were found wearing civilian clothes and one of the dead was a woman, al-Karbouli said, reported the Associated Press.
Iraqi troops found 15 headless bodies in a building inside an abandoned former army base in Latifiya, south of Baghdad, also on Tuesday, said Defense Ministry Capt. Sabah Yassin. The bodies included 10 men, three women and two children. The identities of all those found were not known.
Yassin said some of the dead men in Latifiya were thought to have been part of a group of Iraqi soldiers who were kidnapped by insurgents in the area two weeks ago, according to the AP.
The news of the gruesome discoveries came as insurgents continued stepped-up attacks throughout the country.
In Baghdad, interim Planning Minister Mahdi al-Hafidh escaped an assassination attempt after gunmen opened fire on his convoy. One of his guards was killed and two others injured, police said.
A U.S. soldier was killed and another wounded Wednesday when a roadside bomb detonated as they were patrolling in the capital, the military said.
In another attack in the capital, a suicide bomber detonated a garbage truck packed with explosives outside a hotel used by Iraqi police and foreign contractors, killing two policemen, Reuters reported.
The U.S. Embassy said 30 American contractors were among the 40 people wounded in the blast, which blew a large crater in the road outside the Agriculture Ministry and the Sadeer Hotel used by Western contractors.
Al-Qaida's wing in Iraq, led by Jordanian militant Abu Musab al-Zarqawi, took responsibility for the attack in an Internet posting, calling the Sadeer the "hotel of the Jews," according to the AP.