According to SKY NEWS, a petition calling for him to be pardoned, which was started on Sunday, had more than 42,000 signatures by Tuesday morning and was rising steadily.
The petition says: "Edward Snowden is a national hero and should be immediately issued a full, free, and absolute pardon for any crimes he has committed or may have committed related to blowing the whistle on secret NSA surveillance programmes."
The petition on the We The People pages of the White House website needs 100,000 signatures to be considered by the Obama administration.
A second petition calling on President Barack Obama to take part in a live, public debate with Mr Snowden has fewer than 3,500 signatures.
Separately, the Guardian journalist behind the story, speaking in Hong Kong, said that there will be more to come from the documents.