The new charter would lead to parliamentary and then presidential elections by mid-2014 according to a timetable set by military-installed president Adly Mansour after Morsi's overthrow in July.
"According to the presidential decree... The new document ... Will be subject to referendum ... Expected within two weeks after finishing our task," Mohamed Salmawi said at a press conference.
The 50-member panel started its work on September 8, with 60 days to finalise the document, according to Mansour's timetable.
He said each article had to be approved by at least 75 percent of the panelists for it to be incorporated in the constitution.
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Most of the controversial issues were still under discussion, such as the status of army whose budget was never open for scrutiny under previous constitutions, he added.
The military, led by General Abdel Fattah al-Sisi, ousted Morsi on July 3 following massive protests demanding the Islamist's resignation after a year in office.
Salmawi said the other sensitive issue was military trials for civilians, which were allowed in some cases under Morsi's constitution.
"There is a very strong opinion inside the committee, and also outside, against military trials of civilians. The general feeling is not very sympathetic" towards such trials, Salmawi said.
Several Egyptian human rights organisations have condemned military trials of civilians, saying that about 60 convictions have been passed by army tribunals since July 3.
Another issue to be decided is whether candidates in upcoming parliamentary elections will run as individuals or on party lists.