Those urging Gen Sisi to run for president have been much in evidence at recent demonstrations
Egypt’s interim government has announced presidential elections have been moved forward.
This means parliamentary polls will happen later, not first as originally envisaged by the military-backed authorities’ “roadmap” to democracy.
The move is like to intensify speculation over whether army chief Gen Abdel Fattah al-Sisi will stand.
Many have urged to him to stand after he led the removal of Islamist President Mohammed Morsi last July.
Mr Morsi, Egypt’s first democratically elected president, was deposed after mass protests against his rule.
Interim President Adly Mansour announced the decision to bring forward the presidential poll in a televised speech, saying the decision had been taken after dialogue with “national forces and representatives of various orientations and trends”.
Supporters of the military held rallies on Saturday to mark the third anniversary of the uprising that toppled President Hosni Mubarak in 2011.
Thousands gathered in high-profile locations including Tahrir Square – the focal point of the 18-day 2011 popular revolt – many waving Egyptian flags and banners showing army chief Gen Sisi.
Anti-government protests also took place, with 49 people killed in clashes and arrests reported in several cities.
Amidst continuing violence and instability, many Egyptians believe Gen Sisi is the strong man the country needs, the BBC’s Arab affairs analyst Sebastian Usher reports.
But others are concerned that if he stands and wins – which seems the likeliest outcome – it will make him too strong, giving him all but complete control of the now modified roadmap, our correspondent adds.
The Anti-Coup Alliance, led by Mr Morsi’s Muslim Brotherhood, has called for 18 days of protests beginning on Saturday, mirroring the 18 days of protests that three years ago led to Mr Mubarak stepping down.
The Brotherhood has regularly held protests since the overthrow of Mr Morsi. Hundreds of its supporters have been killed, and thousands detained.
It has been declared a “terrorist organisation” and accused by the interim government of being behind a string of violent attacks in recent months, which the Brotherhood denies.
The crackdown on the Brotherhood has been accompanied by an increasingly hostile climate towards anyone perceived as anti-military, including journalists and secular activists. Many fear the security state in charge during Hosni Mubarak’s era is now firmly re-establishing itself.
Earlier this week human rights pressure group Amnesty International said in a report Egypt has seen violence “on an unprecedented scale” since the army ousted Mr Morsi.
It accused security forces of regularly committing abuses and said rights and liberties in Egypt were being eroded.