"We're conducting a comprehensive inspection," said a police officer on the scene overseeing the raid. "There is no repression going on here."
Church officials said police, some armed with automatic weapons and bulletproof vests, arrived at about 9 a.m. at the three-story wing of a factory that the group rents out as its Moscow headquarters.
Police officials were continuing the raid 12 hours later when a Reuters correspondent was allowed to visit the building with police escort. A second building nearby was also subject to a raid, police and church officials said.
In a statement, the Scientology Church of Moscow described the raids as an attack on freedom of religion.
"Actions by the state to repress religious freedom do not allow Russia to move forward. On the contrary, Russia is moving backwards to totalitarianism," the statement said.
Russia has adopted a controversial law limiting the activities of "non-traditional" faiths, although it was not immediately clear whether Thursday's raids were connected with implementation of that law.
Moscow prosecutors are presently seeking to ban the Jehovah's Witnesses group in a court case which is being closely monitored by human rights activists.
The overseeing police officer on the scene of Thursday's raid on the Scientology headquarters, who declined to be named, said officers were checking everything from tax records to weapons.
"Any organization can be inspected, any factory, any enterprise," he said. "Public organizations are in a special situation. Many don't pay taxes and get around customs."
"But I think everything will be in order here; there's nothing criminal around here."
Interfax news agency said municipal police, State Security Service and tax police forces were all involved in raids on four Scientology offices in Moscow.
Anna Kornayeva, an instructor at the church headquarters, said that about 60 people worked in the battered facility of aging linoleum floors and walls covered with art propagating the teaching of American science fiction writer and Scientology founder L. Ron Hubbard.
One photograph showed Kornayeva and other Russians with actor John Travolta, a prominent member of the faith.
She said the center made its money by charging for classes and had as many as 300 students.
Scientology has been the subject of controversy in some countries, most prominently in Germany where officials have attempted to curb its activities.
The web site of the Scientology Church lists dozens of offices across Russia.