"You are the source of legitimacy, and whoever is protected by anyone else will lose," he told his supporters.
He also addressed popular demands, vowing to work for the release of Omar Abdel-Rahman, the blind sheikh jailed in the United States for a plot to blow up New York landmarks, as well as detained Egyptian protesters facing military tribunals.
"I will do my best to free all detainees, including Dr. Omar Abdel-Rahman," he said, pointing to a group of protesters holding a poster of the spiritual leader of men convicted in the 1993 World Trade Center bombing. Supporters have called for the sheik to be repatriated to Egypt on humanitarian grounds.
Morsi, 60, a U.S.-trained engineer, narrowly defeated Ahmed Shafiq, Hosni Mubarak's last prime minister and a former air force general, in a runoff race that deeply polarized the nation. Initially put forward as a backup candidate for the Muslim Brotherhood, he addressed the crowd with a booming voice, flanked by several security guards.
His victory has given Islamists a new boost after they overcame decades of suppression and arrests under Mubarak's secular regime to become Egypt's most influential post-revolutionary political force. However, the military has fought to check the Brotherhood's rise and maintain its hold on the reins of power.
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."
Many protesters had called for Morsi to hold his swearing-in ceremony in the square, the epicenter of mass protests that ousted Mubarak, but the military generals said it must be held in front of a high court, in the absence of a parliament. The ceremony was scheduled to be held Saturday.
The ruling generals have promised to transfer power to an elected president by Sunday. But they also have given themselves sweeping powers that undercut the authority of the president.
