Activists say at least nine cases of sexual assault were reported last week as revellers celebrated Sisi's presidential election victory and inauguration.
But a graphic video footage of a woman being sexually assaulted at Cairo's Tahrir Square during the celebrations triggered outrage in Egypt and abroad after it was shared widely on websites including YouTube, Facebook and Twitter.
The footage, apparently filmed on Sunday using a mobile phone, shows a mob of men surrounding the young woman, who was stripped of her clothes and badly bruised in the assault.
"Gruesome sexual attacks on women marred President Sisi’s election and inauguration," said Rothna Begum, women's researcher at Human Rights Watch in a statement on Friday.
"Egypt’s women, and the world, are watching to see what President Sisi will do to put a halt to the sexual attacks and harassment," she said, urging a comprehensive national strategy to combat violence against women.
Egypt, which had no specific law on sexual harassment, only recently approved penalties for such offences to include jail terms, fines or both.
Egyptian rights organisations have called for a demonstration against sexual violence on Saturday.
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Sisi urged YouTube to remove the video of the sexual assault.
"The Egyptian embassy in Washington DC and a number of Egyptian authorities, at the direction of President Abdel Fattah al-Sisi, have requested the YouTube adminstration to remove the video of the sexual assault victim," a statement from his spokesman said.
The footage was still on YouTube late Friday, however.
Sisi's request came after the victim herself urged him to do so when he visited her in hospital.
Officials said that police have arrested seven men suspected of sexually assaulting women during Sisi celebrations, but it was unclear whether the group carried out the attack shown in the video.
Since the revolution that toppled long-time president Hosni Mubarak in 2011, the problem of sexual harassment has worsened, with women now regularly attacked during rallies by groups of men in and around Tahrir Square, the epicentre of protests.
Sisi, the former army chief who deposed Islamist president Mohamed Morsi last July, was sworn in on June 8 amid mass celebrations organised by the authorities, after winning last month's presidential election in a landslide.