The nine groups, which include Human Rights Watch and the Committee to Protect Journalists, said on December 6 that the gesture would demonstrate Tashkent's commitment to reform.
The statement named dozens of potential candidates for release, noting that many of them are suffering from ill-health and have been mistreated in detention.
The statement comes a day after the Uzbek Senate adopted a resolution on amnesty connected with the constitution's anniversary.
The amnesty proposed by Uzbek President Islam Karimov applies to individuals convicted for minor crimes, among others.
Uzbekistan often marks Constitution Day, which takes place on December 8, with prisoner amnesties, but beneficiaries typically do not include people jailed on political grounds.