Protesters also tried to gather in Qus in southern Egypt but police dispersed them, security sources said.
There was no demonstration at Tahrir Square, as police closed all roads leading there, or in other parts of central Cairo. Tahrir Square was the epicentre of protests that led to the overthrow of former President Hosni Mubarak in 2011.
Security forces have stepped up their presence in main squares in major cities and plainclothes police have been checking motorists' and pedestrians' mobile phones for political content, measures that continued on Friday.
Sisi, who was in New York this week attending the U.N. General Assembly, returned to Cairo on Friday morning, where he was greeted off his plane by senior ministers and later stopped to speak to a crowd of supporters on the roadside.
Asking them why they were up so early on a Friday, the first day of Egypt's weekend, he said: "The situation isn't worth it. You need to know that the Egyptian people are very aware ... Don't worry about anything."
Sisi also appeared to repeat his earlier rejection of allegations of corruption posted online by Mohamed Ali, a former contractor and actor, in the run-up to the protests. Ali's videos have attracted a wide following.
"This is an image being painted as was done before, comprised of lies and defamation and some media working to present an image that isn't true," he said.
Since last weekend's protests, authorities have carried out a campaign of mass arrests that has resulted in the detention of about 2,000 people, according to rights monitors. Egypt's public prosecutor said on Thursday that "not more than 1,000" had been questioned in the presence of lawyers after participating in protests.
Ali's calls for new protests on Friday were countered by calls for pro-Sisi, "pro-stability" rallies, the largest of which was held along a major Cairo highway that had been cordoned off east of the city centre.
HEAVY POLICE PRESENCE
Buses ferried people including company employees from Cairo and other cities to the rally, where crowds waved Egyptian flags and pictures of Sisi. Delta Sugar Company, a state firm, said it had bussed in workers from its factory in the Nile Delta and offices in Cairo.
Last weekend's protests unnerved investors and led to a pro-Sisi campaign in Egypt's strictly controlled media, which have tried to tarnish Ali's image and that of Egypt's enfeebled opposition.
There was a heavy police presence on Friday around Tahrir Square and at some junctions in central Cairo, including vehicles with water cannon. Many shops and several central metro stations were closed.
At Cairo's Al-Fateh mosque, a starting point for protests in 2011, dozens of police, some in uniform and others in plain clothes with masks and large guns, stood near the exit as prayers finished. At least 20 security vehicles were stationed around the mosque or patrolling nearby.
Police also closed off an area outside Sidi Bishr mosque in Alexandria where protesters had gathered last week, and shut a square in the Red Sea city of Suez where there were protests on Saturday to traffic, witnesses said.
Sisi came to power after leading the overthrow of Islamist former President Mohamed Mursi, a Muslim Brotherhood leader, in 2013 after mass protests against Mursi's rule. On Friday, he said that at some point he would request another "mandate," and Egyptians would "go out in their millions".
Sisi has overseen a crackdown on dissent that has extended to liberal as well as Islamist groups, and which rights groups say is the most severe in recent memory. Muslim Brotherhood leaders have been imprisoned or fled abroad.
His backers say the crackdown was needed to stabilise Egypt after the turmoil that followed the country's 2011 uprising.
Several hundred of those detained in the past week - who include prominent writers, activists and opposition figures - have been placed under investigation for charges including using social media to spread false news, joining a banned terrorist group, and protesting without a permit, defence lawyers say.
U.N. High Commissioner for Human Rights Michelle Bachelet called on Egyptian authorities on Friday to "radically change their approach to any future protests."
(Additional reporting by Amina Ismail, Mohamed Abdellah, Amr Dalsh, Patrick Werr, Nadine Awadalla, Ulf Laessing and Stephanie Nebehay Writing by Aidan Lewis and Ulf Laessing Editing by William Maclean and Matthew Lewis) ((Aidan.Lewis@tr.com; +20-1001174410;))