According to Glen Greenwald of The Guardian, the documents would reveal sensitive information on the NSA, which would allow someone to evade the program or even replicate it.
"In order to take documents with him that proved that what he was saying was true he had to take ones that included very sensitive, detailed blueprints of how the NSA does what they do," Greenwald said in Brazil, adding that the interview was taking place about four hours after his last interaction with Snowden.
Greenwald said he believes the disclosure of the information in the documents would not prove harmful to Americans or national security, but that Snowden has insisted they not be made public.
"I think it would be harmful to the U.S. government, as they perceive their own interests, if the details of those programs were revealed," Greenwald said.
Snowden is stuck in Moscow's airport. He's reportedly willing to meet President Vladimir Putin's condition that he stop leaking U.S. secrets, if it means Russia would give him asylum, until he can move on to Latin America.
The Associated Press contributed to this report.