"Three people carrying American nationality were kidnapped while they were in Dura... inside a suspicious apartment," the spokesman said in a statement.
"Security forces have begun searching for them," the spokesman said.
A police colonel said on condition of anonymity that an Iraqi translator took the Americans for "drinking and women" at an apartment he owned in the Dura area.
Militiamen "attacked the place", the colonel said, adding that "they were kidnapped from inside the apartment, not from the street."
Brothels and alcohol shops have been repeatedly targeted by powerful Shiite militia groups that are now playing a major role in combating the Islamic State jihadist group, which overran large parts of Iraq last year.
