Egypt's newly sworn-in president has apologised in person to a woman who was sexually assaulted by a mob during celebrations marking his inauguration.

Local television networks showed a visibly moved Abdel-Fattah el-Sissi visiting the woman in a Cairo hospital.

"I have come to tell you and every Egyptian woman that I am sorry. I am apologising to every Egyptian woman," said el-Sissi, a former military chief who ousted the country's first elected president nearly a year ago.

Several women were assaulted during Sunday's inaugural festivities. 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.

El-Sissi said it was unacceptable for sexual assaults to take place in Egypt.

"I tell the judiciary that our honour is being violated on the streets and that is not right. It is not unacceptable, even if it is one case," said the president, who spoke a day after he ordered a crackdown on sexual harassment, which he described as an "alien phenomenon" in Egypt. He also called for the restoration of the "real and moral" values of the country's streets.

Sexual harassment has long been a problem in Egypt, but assaults have increased dramatically over the three years since the ouster of long-time 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.

The Interior Ministry, which is in charge of police, said on Monday it had 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 a statement issued by the nation's chief prosecutor, Hesham Barakat.