"Over the past few days, more than 20 bodies, some of them decapitated, were found in Aziziyah town," the officer said on condition of anonymity.
"They were corpses of civilians and sometimes decapitated," he said on Saturday. "Just today, we discovered the body of a woman floating in the river."
An AFP correspondent saw two decapitated bodies in the town on Thursday.
The bodies have been found trapped in a net strung across the river to stop the spread of a fast-growing river weed that chokes the channel, he said.
Recently, the Tigris washed up
57 bodies of men and children
Ten days ago, a police lieutenant colonel based in Suwayrah, about 40 km south of the capital, said that the Tigris had recently washed up 57 bodies of men and children in the area.
Unconfirmed reports two weeks ago from the town of al-Madain, on the southern outskirts of the capital, suggested that armed men had seized Shia hostages in the town and were forcing others to flee.
When Iraqi and US forces entered al-Madain in a show of force a few days later, they failed to find any evidence of hostage-taking but some government officials said the bodies floating down the Tigris were likely those of executed hostages.
However, medical staff who checked the bodies contested this saying that many of the dead had died much before the al-Madain episode.
Dr Falah al-Parmani, head of the Suwayra health department,said the decomposition suggested that the corpses had been killed two weeks before the al-Madain incident.
"I have several names of people being kidnapped and disappeared reported to me from al-Madain over the last few days"
government security adviser
"So there is no way to link the two incidents," he said.
Meanwhile, according to Muwaffaq Rubaie, a government security adviser, several more people have been reported missing from the al-Madain area in recent days.
"I have several names of people being kidnapped and disappeared reported to me from al-Madain over the last few days," Rubaie said.
Rubaie did not give a specific tally of missing people.
Anti-US fighters who fled Sunni strongholds during recent US raids have moved into farming communities to the south to create a series of safe havens to plot attacks on Baghdad, outgoing Interior Minister Falah Naqib had earlier said.