The holiday features celebrations, crowded public squares and widespread harassment of women by men.
Rights activists have faulted Morsi's Islamist government for failing to take action against the wave of sexual assaults. Earlier this month, around 200 activists gathered outside the presidential palace, chanting slogans against Morsi and his Muslim Brotherhood pressing for a law to criminalize harassment. Morsi's order Tuesday appeared to be an attempt to counter the charges of activists.
Complaints about the problem, which has long been a feature of Egypt's society, gained prominence during last year's popular uprising that unseated longtime President Hosni Mubarak. Women activists and reporters told of severe assaults by men in Tahrir Square, the focus of the mass protests.
Activists say little, if anything, has changed.
A prominent activist, Azza Suleiman, told the state-owned Al-Ahram newspaper Tuesday that her two sons were assaulted in downtown Cairo during the holiday while trying to protect a group of foreigners, while police stood by watching the incident. She criticized the police and the Interior Ministry for failing to secure the crowded streets.
Tahrir Square, the center of last year's uprising, has been the scene of a number of assaults against women both protesters and journalists in the aftermath of the revolution. Earlier this month, a correspondent for France 24 TV was "savagely attacked" near Tahrir after being seized by a crowd, the network said.
Last week, Egyptian Prime Minister Hisham Qandil condemned sexual harassment in remarks on his Facebook page, calling it a "catastrophe" that threatens society. Qandil said the Cabinet was preparing a law to impose harsher penalties for sexual harassment. Rights activists have been campaigning for such legislation for years.
Hani Henry, a psychology professor at the American University in Cairo, said that the widespread notion that women should dress more conservatively in order to reduce sexual harassment on Egypt's streets is one of the biggest impediments to addressing the issue.
"There's a 'blaming the victim' mentality," Hany said. He predicted that addressing sexual harassment in Egypt's could be more difficult now that Islamists have emerged as the strongest political power in post-revolutionary Egypt.