The companies that receive the surveillance requests from law enforcement should also be able to release information, the group said in a statement Thursday.
The Global Network Initiative, which includes Facebook and Google, wrote their request to the Freedom Online Coalition, a group of 21 countries that are working to advance Internet freedom, The Hill said.
Google's Transparency Report includes records on seven of the 21 countries in the Freedom Online Coalition over the second half of 2012.
The United States has issued 8,438 requests for Google data.
The U.K., Germany and France issued 1,485, 1,550 and 1,693 requests, respectively. The Czech Republic, Canada and Mexico issued 51, 77 and 90 requests, respectively.
The request comes as the group Human Rights Watch called for governments to protect online privacy.
The group issued international principles to guide governments on how to monitor surveillance practices.
"There is an urgent need to overhaul national surveillance practices to protect everyone's privacy, or risk severely limiting the potential of the Internet," the initative said in a statement released Friday.