In a televised address, Adly Mansour also sought to assure Egyptians that state institutions, including his office, would not interfere in tomorrow's and Tuesday's voting.
"Let us all come out tomorrow and the day after to express our free choice. Choosing, without being guided or dictated to, the person we trust to have the ability to build and run the nation," Mansour said.
Former military chief Abdel-Fattah el-Sissi is the heavy favorite to win the election. His only rival is leftist politician Hamdeen Sabahi, who placed a strong third in the last presidential election held in 2012.
El-Sissi led the military takeover that ousted last July the Islamist Mohammed Morsi, Egypt's first freely elected president, replacing him with Mansour, a career judge.
"The state's institutions, with the presidency at their heart, stand at an equal distance from the two presidential candidates. They have not and will not direct any citizen to a specific choice. Instead, we are all concerned with security and a wide popular participation," Mansour said in the recorded five-minute address.
El-Sissi has since last July enjoyed the support of the media, both state-owned and private, as he rode a wave of nationalist fervor that expressed adulation for the military as the nation's most reliable and strongest institution.
The military-backed government he installed since Morsi's ouster has since cracked down on Morsi's Muslim Brotherhood, the Islamist group he hails from, arresting thousands and killing hundreds.
El-Sissi, apparently for security reasons, did not campaign on the streets, restricting his activity to TV interviews and meetings with various interest groups. Sabahi, on the other hand, has crisscrossed the country, marketing himself as the "candidate of the revolution," a reference to the 2011 uprising that toppled the regime of longtime autocrat Hosni Mubarak.
In separate development, a suspected member of an al-Qaeda-inspired group has been killed by his own roadside bomb in Egypt's restive Sinai Peninsula, according to Egyptian security officials.
They said the militant's father lost an arm in the blast on Saturday. Both men, they added, are members of Ansar Beit al-Maqdis, a militant group which has been blamed for some of the bloodiest attacks in Egypt in recent years.
The officials said the two were trying to plant the bomb on a road frequently used by the army. They spoke on condition of anonymity because they are not authorized to brief journalists.