Opponents of the president joined hundreds already camped out in Cairo's Tahrir Square where tents have been pitched and anti-Morsi banners hung on walls.
Protesters also gathered outside the presidential palace, close to the neighbourhood where thousands of Morsi supporters vowed to pursue a counter-demonstration to defend their president.
Anti-Morsi demonstrations are also expected in provincial cities.
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.
A senior security official said the Suez Canal, the vital waterway that connects the Mediterranean with the Red Sea, has been placed under "maximum security."
The streets of Cairo were unusually quiet on Sunday, the first day of the working week in Egypt, with banks and most offices closed ahead of what Morsi's opponents promised would be a "second revolution".
The grassroots movement Tamarod -- Arabic for rebellion -- is behind a campaign that claims to have collected millions of signatures to a petition demanding Morsi's resignation and new elections.
Posters calling on people to join the protests against his rule have sprung up around Cairo, plastered on walls and stuck on car windows, along with "June 30" graffiti.
The week leading up to the showdown has already seen eight people killed, including an American, and scores more injured as protesters from both sides took to the streets.
Morsi, previously a senior Muslim Brotherhood leader, is Egypt's first freely elected president, catapulted to power by the 2011 uprising that ended three decades of authoritarian rule by Hosni Mubarak.
His opponents accuse him of betraying the revolution by concentrating power in Islamist hands and of sending the economy into free fall.
But his supporters say that many of the challenges he faces he inherited from a corrupt regime, and that he should be allowed to serve out his term which ends in 2016.
Any attempt to remove him from office, they say, is a coup against democracy.
But leading opposition figure, Nobel laureate Mohamed ElBaradei, urged the president "to listen to the people" and step aside.
The fervent displays of emotion from both camps highlight the deep divisions in the Arab world's most populous country.
The army, which led a tumultuous transition after the revolt that ousted Mubarak, has warned it will intervene if there is major unrest.
Since taking office, Morsi has battled with the judiciary, the media and the police. The economy has taken a tumble, investment has dried up, inflation soared and the vital tourism industry has been battered.
Egyptians have been stocking up on food and withdrawing cash in anticipation of Sunday's rallies and, adding to the tension, fuel shortages have caused long queues outside petrol stations, bringing some parts of the capital to a standstill.
On Saturday, at least eight deputies resigned from the Islamist-dominated Shura Council, in a boost for Tamarod which says it now has 22 million signatures to a petition demanding a snap election and Morsi's departure.
The figure, which compares with the 13.2 million votes to 12.3 million by which Morsi won election last year, cannot be verified.
Morsi's camp is determined to defend his legitimacy.
"We will not allow a coup against the president," senior Brotherhood leader Mohamed al-Beltagui told a Cairo rally.
Demonstrator Kamal Ahmed Kamel echoed his comments. "It's not just about Morsi, it's about legitimacy and the state. We can't go backwards," he said.
Others called on the opposition to invest their energy in the political process.
Morsi's opponents reject the idea that removing him is a "coup", saying calls for his resignation are aimed at bringing the revolution back to its cornerstones of democracy, freedom and social justice.
Some said they wanted Egypt to be run by a presidential council and a government of national unity.
"The Islamists have been in power for a year and they proved they failed at running the country," said one, Adel al-Amir.
In a televised speech on Wednesday, Morsi warned the polarisation threatened to "paralyse" Egypt as he tried to placate protesters with promises of constitutional reforms and appeals for dialogue.
Speaking in South Africa, US President Barack Obama voiced concern at developments in Egypt and urged Morsi and his opponents to be more "constructive."
"Everybody has to denounce violence. We would like to see the opposition and President Morsi engage in a more constructive conversation about how to move their country forward."