Despite winning Egypt's first presidential polls after the popular uprising which toppled longtime president Hosni Mubarak, 60-year-old Mursi's name was not removed from the lists of people banned from leaving the country.
"The name Mohammed Mursi is still on the travel ban lists in all Egyptian airports and harbours as a member of the Muslim Brotherhood," the Al-Arabiya reported.
The president will need to file a lawsuit to have his name removed from the travel ban lists, the paper said.
However, the fact that he is still officially banned from traveling is not expected to hinder Mursi from making international trips as the country's president, it said.
Iran has invited Mursi to a summit of Non-Aligned Movement nations to be held in Tehran in late August. Mursi has expressed his keenness to attend the summit.
Travel bans constituted one of several ways the Mubarak regime used to put pressure on Islamists, particularly the outlawed Muslim Brotherhood.
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According to the Egyptian Passports Authority, the total number of Egyptians whose names are placed on travel ban or on watch lists had reached 21,000 in March 2012.
A large number of Muslim Brotherhood members were on the travel ban lists, including group's Supreme Guide Mohammed Badei, Mahdi Akef and Deputy Chairman of the Freedom and Justice Party Essam al-Erian.
Mursi was detained twice in 2006 and 2011 and put under house arrest during the previous regime.