Up to 50 people have been seized from the offices of an Iraqi security firm by people wearing police uniforms.
The 18 bodies found in the van were taken to a morgue
It is unclear whether they have been arrested or kidnapped. An interior ministry official said police had no involvement in the Baghdad raid.
But other officials are reported as telling reporters that the men had been arrested by police commandos.
Earlier the bodies of 18 men were found in a van parked in a western, mainly Sunni district of the city.
The raid on the private security firm al-Rawafed took place in the eastern Zayouna district of the city.
Eyewitnesses and police in the area report seeing up to 50 staff being taken away from the firm's compound in police pick-up trucks.
One interior ministry official told the BBC the raid was being investigated, but that those responsible were not associated with the Iraqi police.
However, Reuters news agency says unnamed officials have told its reporters that the firm's employees had been arrested by police commandos.
The BBC's Andrew North in Baghdad says that if this is confirmed, the raid may be linked to recent remarks by Iraqi Interior Minister Bayan Jabr calling for more control over the rising number of private security firms.
There are thought to be at least 250 such companies in Baghdad, increasingly taking over from Western security contractors.
But another concern is that the raid may be linked to one of the militias operating in Baghdad, our correspondent adds.
The 18 men found dead in an abandoned minivan were bound and blindfolded.
The van was discovered on the road between Amiriyah and Khadra - two mainly Sunni districts of west Baghdad.
Police said the bodies had no identification papers on them. Some reports said two of the men looked like foreign Arabs
The bodies have been taken to a morgue at the city's Yarmouk hospital.
Hospital sources told the Associated Press news agency that the deaths appeared recent and that two of the victims had been shot, while the others were strangled.
"We found a rope round the neck of one of the  victims," a hospital source told Reuters news agency.
In a separate incident, two other bodies were found in east Baghdad tied up and shot.
Iraq has suffered a rise in sectarian attacks since a Shia shrine was bombed last month - but it is not clear if this was the cause in either case.
However, the dumping of bodies has previously been a sign of the violence between minority Sunni Arab and majority Shia groups.
The bombing of the shrine at Samarra on 22 February - and subsequent reprisals in which more than 400 people died - have sparked fears of civil war.