The Constitution Party, headed by reform campaigner Mohamed ElBaradei, will on Thursday reveal an alternative constitution that it hopes to present to the people if the official draft is rejected in a national referendum.
Egyptian expatriates began voting in the poll on Wednesday and will continue until Saturday. Voting inside Egypt will begin on Saturday in half the country, with the second half voting a week later on 22 December.
The party had been formulating the draft with a number of other parties and legal experts for three months, Al-Ahram Arabic website reported on Thursday.
The National Salvation Front, an umbrella group of opposition figures, including ElBaradei and former presidential candidates Hamdeen Sabbahi and Amr Moussa, announced on Wednesday they would vote against the draft constitution.
ElBaradei said via Twitter on Wednesday that the ruling regime's determination to hold the referendum despite widespread protests showed a "lack of responsibility."
"To insist on holding a referendum while the nation is clearly divided, where public dissent is boiling, where there is a lack of judicial and security backing, shows a lack of responsibility towards the national interest," he asserted.