Avaaz launched the campaign a month ago, hoping to gain more than one million signatories but now the group has revised its target to 1.25 million.
The organisation believes the fugitive Snowden should "be recognised as a whistleblower acting in the public interest - not as a dangerous criminal" after the former National Security Agency contractor disclosed details of a vast intelligence operation monitoring millions of phone calls and emails worldwide.
Brazilian President Dilma Rousseff slammed Washington after it emerged US surveillance had extended to calls from within her own office as well as major state firms such as oil giant Petrobras.
Rousseff cancelled an October visit to the United States in protest but has not commented on the possibility of offering Snowden asylum.
The Avaaz petition was started by Brazilian David Miranda, partner of Brazil-based US investigative reporter Glenn Greenwald, who published the Snowden leaks in Britain's Guardian newspaper.
