The American Civil Liberties Union and Amnesty International are ready to launch the "Pardon Snowden" campaign.
They are urging President Barack Obama to act before he leaves office in January 2017.
The launch this week coincides with the release of an Oliver Stone biopic about the former NSA contractor.
The campaign group has created a website, pardonsnowden.org, though its content remains behind a password-protected login. The campaign has also registered social media accounts in preparation for the launch.
Mr Snowden, who is living in exile in Russia, is expected to speak by video link at the launch.
Amnesty International, one of the supporters of the new campaign, has repeatedly backed Mr Snowden since he released details of mass phone and internet surveillance by his former employer, the NSA.
They have said that no-one should be prosecuted for exposing human rights violations, which, they claimed, is what "indiscriminate mass surveillance of communications" amounts to.
The ACLU acts as Snowden's legal adviser, and has called him "a great American who deserves clemency for his patriotic acts".
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