Democratic Alliance leader Fofi Gennimata on Thursday submitted in Parliament a proposal for legislation that would revoke a scheduled further set of cuts to pensions in January 2019.
The Communist Party is also submitted an amendment seeking the revocation of the same planned cuts.
The moves come as party leaders prepare for a debate on post-bailout austerity in Greece.
According to Democratic Alliance, there is scope for the cuts to be revoked as Greece is forecast to produce primary budget surpluses.
The developments follow comments by European Economic and Monetary Affairs Commissioner Pierre Moscovici during his visit to Athens earlier this week which suggested some flexibility on agreed-to post-bailout austerity.