The transfer is a thorny issue which has already sparked the largest protests since Egyptian president Abdel-Fattah el-Sisi assumed power nearly two years ago.
Riot police backed by armored vehicles took up positions in Cairo's Tahrir Square, the epicenter of Egypt's 2011 uprising, as well as on the ring road, downtown and at a suburban square where at least 600 Muslim Brotherhood supporters were killed when security forces broke up their sit-in in August 2013.
Many of the venues declared by organizers as gathering points were sealed off by police, including the doctors' and journalists' unions in central Cairo, according to witnesses, who spoke on condition of anonymity out of security concerns, AP reports.
The military said in a video released late Sunday that troops were deployed to protect "vital and important installations" and deal with anyone who tries to "harm the people's interests or attempt to ruin their happiness" on Sinai Liberation Day, a national holiday marking the completion of Israel's withdrawal from the peninsula in 1982.
Egyptian warplanes roared over Cairo to mark Monday's anniversary, but the military kept a low profile on the ground except for in the Cairo suburb of Heliopolis, home to military headquarters and the presidential palace. The Interior Ministry said police were out in force to protect "peaceful" citizens who wish to celebrate.
El-Sisi Sunday urged citizens to defend the state and its institutions from the "forces of evil," an apparent reference to the planned protests.
Monday's planned demonstrations would be the second wave of protests this month against the decision to give up control of the islands at the mouth of the Gulf of Aqaba. On April 15, about 2,000 demonstrators protested in downtown Cairo over the islands.
That protest was the largest against el-Sisi since he assumed office in 2014, nearly a year after leading the military ouster of the Islamist Mohammed Mursi, Egypt's first freely elected leader. Chants of "leave," and "the people want to bring down the regime" rang out in the downtown area on that day, harkening back to the 2011 uprising that forced autocrat Hosni Mubarak to step down after nearly 30 years in power.
Authorities have detained dozens of activists in recent days, with the arrests continuing until just hours before the planned demonstrations. Freedom for the Brave, an activist group, says nearly 100 people have been arrested since the latest round of detentions began last week.
Egypt says the islands of Tiran and Sanafir, off the southern coast of the Sinai Peninsula, belong to Saudi Arabia, which placed them under Cairo's protection in 1950 because it feared Israel might attack them. The government says officials and experts have for years negotiated with their Saudi counterparts and agreed that the islands are inside Saudi Arabia's territorial waters.
The announcement came during a visit to Egypt this month by the Saudi monarch, King Salman, as the kingdom announced a multi-billion-dollar package of aid and investment to Egypt, fueling charges that the islands were sold off.
"Egypt needs the truth revealed to its people: Through dialogue, not suppression, with documents, evidence and maps, not security raids and random detentions," prominent columnist Abdullah el-Sinnawy wrote in Monday's edition of the Al-Shorouk daily.
"It's difficult to resolve a crisis like this one through the fist of security, no matter how tough it is."
El-Sisi insists that Egypt has not surrendered an "inch" of its territory and has demanded that people stop talking about the issue.
But the Egyptian leader has faced mounting criticism about other issues as well, including the ailing economy and the abduction, torture and killing of an Italian graduate student in Cairo earlier this year. That incident has poisoned relations with Italy, one of el-Sisi's staunchest EU supporters and Egypt's biggest European trade partner.
Egyptian authorities have denied any involvement in the student's killing.