Tahrir Square and vowed to fight for authority, defying country's ruling generals.
Mursi, who was speaking on the eve of his swearing-in, took the symbolic oath after many protesters called on him to do so to defy the ruling army who took power after Hosni Mubarak's ouster.
He swore to uphold the constitution and “the republican system”, reciting the words of an oath which he will formally take tomorrow in front of the supreme constitutional court. Mursi, 60, in his first public speech promised to be a “president for all Egyptians”, adding: “You are the source of all authority and legitimacy.”
He insisted that “no institution will be above the people,” critiquing an army which has sought to shield itself from parliamentary oversight.
“I promise you that I will not give up on any of the powers given to the president,” Mursi said, in a veiled reference to the Supreme Council of Armed Forces' recent decrees.
At one point he opened his jacket to show the crowd he wasn't wearing a bulletproof vest, saying he “fears no one but God.” His defiant speech was a clear challenge to the army, which also says it represents the will of the people.
“We will complete the journey in a civil state, a nationalist state, a constitutional state, a modern state,” he told the crowd, to applause and cheers.
Mursi promised to end torture and discrimination, and to deliver social justice for millions of Egyptians.
He chanted with the crowd at the beginning of his speech, “Free revolutionaries will continue the course.” “Commissioning me with the presidency is a great honour I'm proud of,” Morsy said.
A wave of emotion swept the Egyptian capital as thousands thronged the iconic Tahrir Square to hear Mursi as a show of angst against the ruling military and a show of support to Mursi, who as president elect is negotiating with the Army the powers his civilian administration will wield.
Mursi also praised crowds in Cairo's Tahrir Square, the focal point of protests that overthrew Mubarak. “The revolution must continue until all is objectives are met,” Mursi said.
Mursi also promised to work to free civilian detainees being tried by military courts and Omar Abdel Rahman convicted in the 1993 World Trade Center bombing.
He also paid homage to Tahrir Square itself, and other squares from which he said “a new, free Egypt emerged.” As president, Mursi said he would remember that he is first responsible to the martyrs of the revolution, “whose blood watered the beautiful tree of liberty.”
He also spoke briefly about Egypt's foreign relations, promising to improve relations with neighbours in Africa and the Middle East, and to “keep the peace”.
“We will never give up the rights of Egyptians abroad,” he said. “Respecting the will of the people is the basis of our foreign relations.”
Spokesmen for the Islamist Muslim Brotherhood, to which Mursi belongs, had previously said he would take his oath before parliament, which was dissolved by the SCAF last week.
The assembly, elected last November, was dominated by the Muslim Brotherhood-backed Freedom and Justice Party (FJP) and other Islamists.
The SCAF issued a declaration giving itself sweeping legislative powers and control over defence policy, and announcing the appointment of a panel to write a new constitution.
Essam El-Erian, vice-president of the Muslim Brotherhood's FJP, said the party would maintain a sit-in at the Tahrir until executive power was handed over to the democratically-elected leader by the SCAF.
While Egyptians have voted over a year after an uprising that ousted Mubarak, many feel the results of the revolution are yet to be consolidated into a civilian rule, as the ruling military appears increasingly reluctant to complete the transition of power.