During his first public address after taking office, Morsi vowed support for Palestinians and what he called their "legitimate rights." He said his administration would continue to honor its international treaties - a reference to the 1979 Egyptian-Israeli peace treaty.
Relations between the two neighbors have become particularly tense since last year's overthrow of Hosni Mubarak, who had forged close ties with the Jewish state during his 29-year rule. The rise to power of Egyptian Islamists has been a source of alarm among many Israelis.
Morsi is the Arab world's first Islamist head of state. He received his Ph.D. at the University of Southern California back in 1982.
The Associated Press contributed to this report.