The Tagammu Party has accused the constitution committee of favouring the rich and ignoring the rights of women, Coptic Christians and Nubians.
The leftist party said the draft constitution does not set spending limits for election campaigns and therefore favours "those with millions."
While the draft maintains the reservation of 50 percent of seats for workers and farmers, it does not include an article making it possible for people from less advantaged backgrounds to contest elections, it said.
The draft constitution ignores the rights of women, Coptic Christians and Nubians for fair representation, and uses electoral freedom as an excuse, it added.
"They forget that we live in a time when women's rights are rejected based on argument from Sharia law, and Copts are being killed because they are Copts and their churches are being burned and destroyed. In such a state how can we expect fair representation for women, Copts and Nubians?"
The party has sent a letter to constitution committee leader Amr Moussa demanding Nubians be granted an independent electoral district. A large number of Nubians live in the El-Nuba region which is part of Kom Ombo electoral district which has a non-Nubian majority.
It also suggested an article stating the president should appoint 40 members to the House of Representatives - 20 women and 20 Copts.
"The party realises the quota is not popular, but we insist it is the only way to achieve fairer representation.
"We warn the constitution committee and the Egyptian people of the dangers of taking this issue lightly. If the next parliament is devoid of women, Copts, Nubians and the poor it will be undemocratic and thus will not guarantee stability."
A 50-member committee is currently amending the 2012 constitution, which was drafted by an Islamist-dominated assembly. The amendments are part of the 3 July roadmap which included the removal of president Mohamed Morsi, who hails from the Muslim Brotherhood.
The amendments are to be finalised and approved by interim President Adly Mansour on 3 December. They will then be put to a national referendum, followed by parliamentary and presidential elections.