The Presidency highlighted that the remaining months of the current transitional period will focus on mobilising funds to ensure the effective implementation of the revitalised peace agreement.
The proposed vote follows years of delays: An election was due to take place in 2015 but was postponed after the young country descended into civil war.
SSOMA said on Monday that it does not want the elections extended or rescheduled and that the peace process - the Tumaini Initiative that is ongoing in Nairobi - should be prioritised.
The country has faced an economic meltdown that experts say could bring not only hardships but also political turmoil to a nation wracked with both.
The civil society group also called for the dissolution of the National Security Service (NSS), advocating for its reconstitution as the National Intelligence Service.
President William Ruto in late March appointed Sumbeiywo as the Chief Mediator for the South Sudan mediation peace process.