Morsi, overthrown by the military on July 3, was placed in detention on July 26 over charges including his alleged links with the Palestinian Islamic resistance movement.
Morsi has been held in military custody in an undisclosed location since then.
On July 26, Morsi was accused of conspiring with Palestinian group of Hamas to carry out "hostile acts" during the uprising that led to the overthrow in 2011 of his predecessor Hosny Mubarak.
At the peak of the uprising against Mubarak, Morsi and more than 30 other leaders of his Muslim Brotherhood group were detained in prison. They were freed along with other inmates in a raid by gunmen.
In June, a court reportedly found that the Muslim Brotherhood leaders had been freed "thanks to an international plot" involving Hamas and local fighters.
On Monday, judges extended Morsi's 15-day detention pending investigation.
Thousands of his supporters have been protesting since his ouster, vowing to continue until he is reinstated. Their biggest sit-ins are in north-eastern Cairo and south of the capital.
The police's threat to break up the two main sit-ins has set the stage for possible violence.
Security officials said at the weekend that police would blockade the sit-ins and use water cannon to disperse the protesters.
However, no security was seen surrounding the squares.
In Rabaa al-Adawiya Square, the Islamists' biggest protest camp, witnesses said the number of women and children declined, as rocks and stones were piled at the entrances to the area, showing that they were bracing for clashes with security.
Men securing the square wore metal helmets and held sticks and iron bars.
Dozens of people have been killed in clashes between Morsi backers and opponents around the country since his ouster.
Rights groups have warned that removing the protesters by force will result in a bloodbath.
NJF/NJF