The charter will be submitted to a referendum early next year that has been billed as the first stage in a "democratic transition" promised by the military-installed authorities following the ouster of Islamist president Mohamed Morsi in July.
The charter in its present form allows the military to prosecute civilians in some cases, appoint the defence minister and keep its budget beyond any civilian scrutiny -- powers reserved by the legislature, executive and judiciary of most democratic countries.
Police fired tear gas to disperse the protesters in Tahrir and another pro-Morsi demonstration near the High Court, the violence underscoring Egypt's lingering polarisation nearly four months after the military deposed Morsi.
Morsi, Egypt's first democratically elected president, was overthrown on July 3, and in mid-August the security forces launched a sweeping crackdown on his supporters which has left more than 1,000 people killed and thousands more jailed.
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His detention is expected to further anger secular activists who are furious over the provisions in the draft charter concerning the military. Another 24 activists also saw their detention extended by 15 days today.
The thorny issue of the insular military's longstanding privileges was at the heart of voting on the constitution today after the 50-member panel drafting the new charter approved 138 of the 247 articles of the basic law the day before.
Several secular activists had demonstrated against the provision, fearing it could be applied to protesters, journalists and dissidents.