Amnesty's call comes after harrowing tales of mob attacks around Cairo's Tahrir Square.
"Horrific, violent attacks on women including rape in the vicinity of Tahrir Square demonstrate that it's now crucial President Morsi takes drastic steps to end this culture of impunity and gender-based discrimination, and for all political leaders to speak out," said Hassiba Hadj Sahraoui, deputy director for the Middle East and North Africa at Amnesty International.
"Impartial, thorough investigations are vital to determine whether these mob attacks are co-ordinated by state or organised non-state actors and ensure perpetrators are brought to justice."
On Cairo's streets, sexual harassment of women, regardless of whether or not they wear an Islamic headscarf, is common in the form of obscenities, touching or groping.
But an increase in accounts of mob attacks, sexual violence against women and even rape have raised the alarm and prompted the creation of several groups to combat the problem.
"The tactics used by mobs in recent protests is a harrowing reminder of the sexual harassment and assault against women protesters under ousted president Hosni Mubarak. Women have been a vital part of protests and have sacrificed much in their fight for freedom and social justice," Hadj Sahraoui said.
"Egyptian authorities need to honour their activism and pull out all stops to address endemic violence against women in all echelons of society."
As Egyptians took to the streets to mark the second anniversary of their uprising on January 25, nearly 25 cases of sexual violence were reported, Amnesty International said.
In a recent statement, the UN High Commissioner for Human Rights Navi Pillay slammed the failure of authorities to prevent acts of sexual aggression.
"I deplore the fact that sexual violence is permitted to occur with apparent impunity in a public square, and that the authorities have failed to prevent these attacks or to bring more than a single prosecution against the hundreds of men involved in these vicious attacks," Pillay said.
?"There has also been far too little effort to grapple with the sexual harassment and sexual violence taking place in a number of Egyptian cities."
Amnesty International said it gathered testimony from women recently attacked by mobs often using weapons in assaults that last from five minutes to more than an hour.
"Given the stigmatisation attached to harassment and sexual assaults against women and the attitudes of law enforcement officials, many cases go unreported. Those who do try and press charges face a wall of indifference and even blame and contempt in their struggle for justice," said Hadj Sahraoui. – Sapa-AFP