The new charter aims to replace the constitution passed under former president Mohammed Morsi months before he was deposed by the army in July, 2013, after nationwide protests against his Islamist regime.
About 53 million Egyptians are eligible to vote for the new constitution in the referendum, the result of which could see General Sisi launch a presidential bid.
Anti-coup protesters, who blame Sisi for the removal of Morsi from the presidency in July, rallied in the capital Cairo, Al-Sharqiyah in the north of Egypt and Fayoum and Delga, in the south.
Tens of thousands of police and army soldiers were deployed across the country to guard the proceedings amid fears of renewed violence after yesterday's deadly clashes in several cities left at least nine dead, Ahram Online reported.
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Security forces were also deployed in Ossim and Giza today after gunmen stormed a polling station.
Minister of State for Administrative Development Hany Mahmoud said today that a random sample of voter turnout in 40 polling stations showed that an approximate 28 per cent cast their ballot yesterday.
The minister also said that the number of polling stations designated to those who live away from where they are registered have increased today to reach 19 stations nationwide.
During yesterday's polling, incidents of violence and celebration at polling stations were witnessed, outlining the polarisation that has gripped the country for years.
Despite the sporadic clashes, many voters across the nation remained celebratory and cheerful on the first voting day, with most endorsing the national charter -- a recently-amended version of the 2012 constitution that has been billed as the first step in a wider political transition following Morsi's ouster.
The new charter, drafted by a liberal-dominated committee appointed by the military-backed government, would ban political parties based on religion, give women equal rights and protect the status of minority Christians.