Supporters of ousted president Mohamed Morsi staged demonstrations on Friday in Cairo and elsewhere, amid renewed calls for protests against the interim authorities, Al-Ahram Arabic news website reported.
Tensions were expected to simmer after former army chief Abdel Fattah El-Sisi, who led Morsi's ouster last summer after mass protests against the Islamist president, scored a crushing victory in this week's presidential election.
Security had been heightened nationwide early on Friday on the back of calls by a pro-Morsi grouping for a "revolution week" to "call on the military to return to its barracks."
Security forces used teargas to scatter protests by Islamists in and outside Cairo.
Dozens of Morsi supporters marched in the capital -- including in the eastern Ain Shams district, as well as the southern suburbs of Maadi and Helwan.
Ain Shams has been a major scene of clashes between supporters of Morsi's Muslim Brotherhood and local opponents and police.
In Giza's Haram district – close to the Giza pyramids – and in 6 October city, a satellite development some 30 km outside Cairo, supporters of Morsi's Muslim Brotherhood group formed human chains, held aloft pictures of Morsi, and chanted anti-army slogans.
Riot police intervened to disperse the crowds in some locations, Al-Ahram said.
Since Morsi's removal, authorities have launched a fierce crackdown on Islamists, which has seen hundreds killed in clashes and thousands of others jailed.
Security forces on Friday also dispersed several demonstrations in eastern parts of Alexandria, Egypt's second largest city, a local security official said.
Twenty-five alleged Brotherhood members have been arrested for "rioting", said Nasser El-Abd, a senior police officer in the city.
Riot police also fired teargas to scatter protests in Fayoum, a governorate south of Cairo.
Elsewhere in the country, unknown assailants opened fire on a police station in the North Sinai town of Sheikh Zuweid, state news agency MENA said. No casualties were reported.
In Cairo, a 20-year-old university student was killed when an improvised bomb he was carrying detonated while he was riding a motorbike in Nasr City district.
El-Sisi won over 90 percent of the votes in this week's election, according to preliminary counts, beating sole rival Hamdeen Sabahi.
The official results of the elections are due to be announced next week.