Such calls came one week after mass arrests in the country, with almost a thousand defendants in preventive detention for participating in demonstrations last week, the first against Al-Sisi since 2016.
Mohamed Ali, an Egyptian businessman who has promoted the protests from Barcelona in Spain, released a new video late on Thursday calling for fresh demonstrations on so-called "Salvation Friday", Efe news reported.
Ali, however, warned his countrymen not to gather at Tahrir Square in central Cairo the iconic setting of the 2011 revolution that ended the rule of the country's former President Hosni Mubarak who held power for over 30 years.
"We move from the alleys to the main streets then the marches shall go to the nearest main square. Tahrir is not the target, because all the squares in Egypt are Tahrir squares," Ali said in a video he posted across social media platforms, which also has been broadcast by non-governmental and international TV channels.
He also advised the demonstrators to "get away from any incitement or attempts of confrontation" by Al-Sisi's supporters.
Earlier on Friday, Al-Sisi arrived in Cairo from New York, where he attended the UN General Assembly. Upon landing, he was received by a gathering of people at the airport carrying placards that read "Al-Sisi is my President".
He spoke to the Extra News private TV channel stressing that the people should not worry about anything and urged the media to adhere to its "great duty" by not abandoning simple citizens.
While in New York, Al-Sisi held a meeting with his US counterpart Donald Trump, in which the Egyptian leader blamed so-called "Political Islam" of being the main cause of the region's instability.
Al-Sisi took over the helm of the country in July 2013 after dethroning Mohamed Morsi.
Lawyers and human rights NGOs reported that the charges against the defendants include: "Being part of a terrorist group", "spreading false news and information", "using Internet websites to commit a crime that threatens the public security and peace" and "demonstrating without permission".
( With inputs from IANS )