"It's ridiculous," he said. "A constitution being written by one force and one force alone. We tried our best and there was no use."
Sawiris said two parties, including his and a coalition of secular and left-leaning parties, withdrew from the vote for the 100-member panel, half of which will be senators and parliamentarians.
Lawmakers are to vote for 50 members from the upper and lower houses of parliament, and 50 people outside parliament to sit on the panel.
According to preliminary results of the vote, published by the official MENA news agency, the panel will include 25 lawmakers affiliated to the Muslim Brotherhood's Freedom and Justice Party, 11 lawmakers from the ultra conservative Salafist Al-Nur party and 14 independents or members of other parties.
The 50 members chosen outside parliament include Islamists, several liberal figures, a handful of Copts and a member of the ruling military council, according to MENA and press reports.
Ahead of the vote, at least two other parties had boycotted the voting from the start, including the leftwing Tagammu party.
"The constitution should not reflect the majority, it should reflect all forces in society," said Rifaat al-Said, the head of Tagammu.
"There is an attempt to posses everything," he said of his party's Islamist opponents. "Possessing the constitution is the most dangerous thing."
Mustafa al-Naggar, head of the Adl (Justice) Party, said parliamentarians should not even be on the panel, which will also include 50 public figures.
"Parliamentarians have a special interest," he said.
The constitution will lay out the powers of the legislature, which Islamists dominated in elections after Mubarak's fall.
According to a schedule established by the military, the panel is meant to finish its work before presidential elections, which now seems unlikely ahead of the vote due to be held in May.
Some presidential candidates fear that could leave the new president without constitutionally defined powers, as the dominant Islamist Freedom and Justice Party angles to give more powers to a prime minister in the new charter.
The FJP, the political arm of the powerful Muslim Brotherhood, has been pressuring the military to sack the cabinet and appoint an FJP-led government.
At Saturday's joint session, which began at noon local time (1000 GMT), the lawmakers were each to list 100 members they want appointed to the panel and then cast their ballots in 14 boxes, parliamentary speaker Saad al-Katatni said.
Liberals fear that the Islamists will try to beef up references to Islam in the new constitution.
The old charter said that the principles of Islamic law were the source of legislation, a vague formulation that hardliners in the ultra-conservative Salafi Nur party want clarified in the new constitution.
But the Muslim Brotherhood's FJP has sought to allay fears that it wants a stricter adherence to Islamic law in the new constitution.
In a comment on his Twitter account, Mohamed ElBaradei, the former UN nuclear watchdog chief turned Egyptian dissident, also questioned parliament's right to form the panel.
"A parliament whose legitimacy is in doubt will elect a panel, half of it from parliament, that is not partial to forming a constitution for Egypt rather than for the (parliamentary) majority," he wrote.