A sea of flags fluttered wildly Sunday as tens of thousands of people staged a show of force in Cairo's Tahrir Square to back the army's ouster of Egypt's first freely elected president.

As the crowds grew larger and larger, a military aircraft flew low over the capital, leaving behind it long trails of smoke in black, white and red -- the colours of the Egyptian flag.

"We are on the street to show the world that it was a popular revolution and not a coup that overthrew" Islamist president Mohamed Morsi, said a beaming teacher who gave her name as Magda.

The Tamarod movement, which engineered the massive June 30 rallies that culminated in Morsi's overthrow on Wednesday, had led calls for people to gather at Tahrir and Ittihadiya presidential palace to "complete the revolution".

And the anti-Morsi crowd swelled in the iconic square as people poured in from sidestreets, some unfurling a giant national flag emblazoned with the words "Go away" -- a slogan used widely on June 30.

"Egypt had a revolution, not a coup," read a huge banner wielded by one group of demonstrators.

The protesters could be heard saying the same phrase, again and again.

"Morsi's removal was not undemocratic because 30 million people took to the streets to express their anger," said an engineer who identified himself as Yasser, giving slightly inflated figures for the June 30 protests.

Yasser said he expected a "constitutional declaration" to be made soon which would "launch the new Egypt in which everyone will be included," echoing statements from the interim government.

Others carried portraits of army chief Abdel Fattah al-Sisi, the general behind Morsi's ouster.

There were similar scenes in Alexandria on the Mediterranean and in other major cities across the Arab world's most populous country.

Their Islamist rivals staged counter demonstrations in the capital, where police armed with Kalashnikov assault rifles watched over the pro-Morsi demonstrators.

They converged on Rabaa al-Adawiya mosque, Cairo University and the Republican Guard headquarters for rallies to support the "legitimacy" of Morsi's election in June last year and to "reject the military coup".

Carrying pictures of the ousted president, they erected barricades and set up checkpoints in various parts of the capital.

A throng estimated at tens of thousands of people forced the closure of the main road to the international airport.

Morsi's single year of turbulent rule was marked by accusations he failed the 2011 revolution that ousted autocratic president Hosni Mubarak by concentrating power in Islamist hands and letting the economy nosedive.