The promise of assistance was in an open letter that will be mailed to authorities and be part of an online campaign by the non-government organization Avaaz, which specializes in petitions, the Brazilian newspaper Folha de S. Paulo reported Tuesday.
Folha de S. Paul said it obtained Snowden's letter.
"Many Brazilian senators have asked my help with their investigations into suspected crimes against Brazilian citizens. I expressed my willingness to assist, where it is appropriate and legal, but unfortunately the U.S. government has been working very hard to limit my ability to do so," Snowden, living in temporary asylum in Russia, said the letter.
Snowden said his temporary status, which expires in 2014, gives the United States leverage to bar him from assisting Brazil in its investigation the activities of the NSA in Brazil, including the monitoring of phone calls and emails of President Dilma Rousseff and other Brazilian officials.
"Until a country grants permanent asylum, the US government will continue to interfere with my ability to speak," Snowden said in the letter.
This summer, Snowden leaked to the British publication the Guardian and to the Washington Post documents about the breadth of the NSA's monitoring programs.
"Today, if you carry a cell phone in Sao Paulo, the NSA can track where you are, and does," Snowden said in his letter.
The unfettered surveillance, he said, "threatens to become the biggest human rights challenge of our times."
Snowden has requested permanent asylum in several countries, but said he prefers Brazil, which has not responded to his request, Folha de S. Paulo said.
Snowden said the decision to leak information about the NSA surveillance programs cost him dearly and put him in danger.
"The price of my speech was my passport, but I would pay again," he said. "I prefer to be stateless rather than lose my voice."