The group published a list of 59 people they say were detained since Thursday, arrested at cafes and at their homes in Cairo, adding "the arrests continue".
Opposition groups -- including the April 6 movement, which spearheaded the popular uprising that ousted former leader Hosni Mubarak in 2011 -- have called for the rally mainly in protest at the government's deal to hand two islands in the Red Sea to Saudi Arabia.
The controversial move by President Abdel Fattah al-Sisi has provoked outrage among many Egyptians who accuse him of "selling" the islands in the Straits of Tiran in return for Saudi investment.
On April 15, more than 1,000 people demonstrated in central Cairo in the biggest protest in two years demanding "the fall of the regime", with police firing tear gas to disperse them.
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That protest was called for by both secular and Islamic activists, and while originally about the islands became a wider demonstration against the Sisi government.
Demonstrations not approved by the police have been banned.
Among those arrested in the past 24 hours was prominent rights activist and lawyer Haitham Mohamedin, according to fellow lawyer Rajia Amrane.
Sisi, who won elections in 2014, is reviled by Islamists and secular dissidents, but many Egyptians say they need a strong leader to revive the country's economy after years of unrest.
He had enjoyed unwavering loyalty in much of the Egyptian media since he took office, but criticism of the president and his police force has grown in recent months.