"It is the biggest protest in Egypt's history," the source told AFP on condition of anonymity.
The source said pro-Morsi protesters who gathered at a rival demonstration in Cairo's Nasr City neighbourhood were estimated to number around 25,000.
One person was killed and more than two dozen injured in fighting on Sunday between supporters and opponents of Egyptian President Mohamed Morsi in the Nile city of Beni Suef, south of Cairo, security sources said.
It was the first death reported on a day when hundreds of thousands of opposition protesters took to the streets demanding that Morsi quit, on the first anniversary of his inauguration.
Opponents of President Mohammed Morsi have attempted to storm the headquarters of the Muslim Brotherhood in Cairo, the organization’s spokesman has said.
Violence had been widely anticipated ahead of Sunday’s multi-million countrywide protests against the president on the anniversary of his inauguration, demanding his resignation.
Around 150 "thugs" attacked the building in the Moqqattam neighbourhood with molotov cocktails, birdshot and stones, said Gehad al-Haddad, a spokesman for the Muslim Brotherhood.
Al-Haddad said the attackers were successfully repelled.
Egypt's main opposition coalition on Sunday urged hundreds of thousands of protesters demanding the ouster of President Mohamed Morsi to stay on the streets until their goals are achieved.
In a statement entitled "Revolution Statement 1", they urged "all the revolutionary forces and all citizens to maintain their peaceful (rallies) in all the squares and streets and villages and hamlets of the country... until the last of this dictatorial regime falls."
Thousands of Egyptians demanding the ouster of Egypt's Islamist president are gathering at Cairo's central Tahrir Square at the start of a day of massive, nationwide protests many fear could turn deadly.
Sunday marks the first anniversary of President's Mohammed Morsi's assumption of power as Egypt's first freely elected leader.
Thousands of Morsi's supporters have staged a sit-in since Friday in an eastern Cairo district not far from the presidential palace, the focus of protests later on Sunday to demand his ouster.
Demonstrators streamed into the square, where tents have been pitched and anti-Morsi banners hung on walls.
In Cairo's Nasr City neighbourhood, Morsi's supporters vowed to pursue a sit-in to defend the legitimacy of the president, who assumed power one year ago after Egypt's first free presidential elections.
Police and troops have deployed to protect key buildings around the country, security officials said.
The health ministry said hospitals have been placed on high alert.
More than 22 million people have signed a petition in Egypt demanding the departure of Islamist President Mohamed Morsi and a snap election, the opposition Tamarod (Arabic for rebellion) group said on Saturday.
"Our petition has gathered 22,134,465 signatures," Tamarod spokesman Mahmud Badr told journalists on the eve of Sunday's first anniversary of Morsi's inauguration when it has called for nationwide protests.
This figure is higher than the number of people who voted for Morsi in last year's presidential election -- 13.23 million, or 51.7 percent of the ballots cast.
Previously, Tamarod said 15 million people in Egypt had signed the petition demanding that the president step aside.
Morsi supporters have dismissed the petition as invalid, insisting that only elections can decide whether a head of state stays or goes. His term of office is due to end in 2016.
The country was bracing on Saturday for the protests marking the first anniversary of Morsi's term in office amid violence in which several people have been killed, including a young American.
Opposition protests have sparked counter-demonstrations by the Muslim Brotherhood and its Islamist allies that have triggered often bloody clashes across the country.
Morsi, 62, stands accused by his critics of failing the 2011 revolution that brought him to power and of ignoring nearly half of the electorate of around 50 million who did not vote for him last year.
Voice of Russia, Reuters, RT, AFP, CBS