The attacks were a grim reminder of one of Egyptian society's darkest sides and coincided with el-Sissi starring in carefully choreographed ceremonies held at two of the capital's most opulent presidential palaces and attended by hundreds of local and foreign dignitaries.
Sexual harassment has long been a problem in Egypt, but assaults have increased dramatically in ferocity and in number in the three years since the ouster of longtime autocrat Hosni Mubarak.
Tahrir Square, the birthplace of the 2011 uprising against Mubarak, is the most common site of such attacks amid the large crowds. Women's groups complain that tough new laws have not done enough.
El-Sissi described sexual harassment as an "alien phenomenon" in Egypt and called for the restoration of the "real and moral" values of the country's streets, his spokesman Ehab Badawi said in a statement.
The president instructed Interior Minister Mohammed Ibrahim, who is in charge of police, to do whatever it takes to bring the situation under control, and to honor a policeman who came to the teenager's rescue.
The Interior Ministry has arrested seven suspects ages 15 to 49 in connection with the sexual harassment that occurred during Sunday's celebrations.
Three of those men have been charged with sexual assault under the threat of force and attempted rape, according to the nation's chief prosecutor, Hesham Barakat. A statement from his office said they would immediately be put on trial.
The statement also gave graphic details of the attack, saying the attackers first formed a circle around the two, stripped the mother of her clothes and assaulted her. Later, the mother fell on a bowl of hot water used by a tea maker at the square, sustaining burns on 25 percent of her body.
It said the attackers later turned their attention to the daughter but could not do the same to her because police intervened. The statement did not say whether the daughter was also stripped and assaulted.
Authorities also were examining a dozen videos from security cameras or bystanders who filmed sexual assaults on their cellphones, according to security officials, who spoke on condition of anonymity because they were not authorized to speak to the media.
Last week, authorities issued a decree declaring sexual harassment a crime punishable by up to five years in prison. The decree amended Egypt's current laws on abuse, which did not criminalize sexual harassment and only vaguely referred to such offenses as "indecent assault."
On Monday, 29 women's rights groups released a joint statement accusing the government of failing do enough to address the spiraling outbreak of mob attacks on women and calling for a "comprehensive national strategy" to stop the violence. They said they had documented more than 250 cases of "mass sexual rape and mass sexual assaults" from November 2012 to January 2014.