"These people were not arrested for their faith. The six Bahais are accused of insulting religious sanctities and the Christian citizen of propaganda against the system," Ali Reza Jamshidi told reporters.
He said the detainees' cases were under investigation, but did not reveal their identities or say when they had been arrested.
Jinous Sobhani, the former secretary of Nobel laureate Shirin Ebadi's rights group, is also accused of "propaganda against the system and acting against national security," Jamshidi said.
Fars news agency reported that Sobhani was arrested in mid-January for links with a Bahai organisation.
The Bahai faith was founded in Iran in 1863 but is not recognised by the government. Its followers are regarded as infidels and have suffered persecution both before and after the 1979 Islamic revolution.