The News & Record of Greensboro reported that the order came from Sgt. Craig McMinn in the department's Special Intelligence Unit. The ministers didn't identify the officer who provided the information.
Telephone messages left Tuesday by The Associated Press for McMinn and Chief of Police Timothy Bellamy weren't immediately returned.
On the morning of Nov. 3, 1979, a heavily armed caravan of Klansman and Nazi party members confronted the rally. Five marchers were killed and 10 were injured.
Those charged were later acquitted in state and federal trials. The city and some Klan members were found liable for the deaths in civil litigation.
The Greensboro Truth and Reconciliation Commission released its findings in 2006, after spending two years researching the shootings and surrounding events. Its report placed most of the blame for the violence on Greensboro police who knew the white supremacists planned to attend the "Death to the Klan" march.
But the report also found fault with both the Klan and Nazi members who opened fire and the communist activists who underestimated the danger posed by verbal baiting of the Klan.
The commission, which had neither subpoena power nor the ability to grant amnesty, recommended that the police department and city officials apologize for the department's role in the shootings.