In a video titled "Climbing the Great Pyramid of Giza", Danish photographer Andreas Hvid appears to scale the 4,500-year-old tomb on the outskirts of Cairo at night with an unidentified woman who is later seen taking off her top.
Hvid says the video was taken in late November but it was published on YouTube on December 8.
A photograph released by Hvid appears to show the couple completely naked on top of each other while looking in the direction of a nearby pyramid with the horizon illuminated.
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"The public prosecution is investigating the incident of the Danish photographer and the authenticity of the photos and video of him climbing the pyramid," Mostafa Waziri, the secretary general of Egypt's supreme antiquities council, told AFP.
The nearly three-minute video has taken social media by a storm and has been the subject of late night talk shows. It amassed more than 2.6 million views on YouTube alone.
"A 7,000-year-old civilisation has turned into a bed sheet," a Twitter user said.
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The authenticity of the images has been disputed with some arguing that the photograph showing the pair naked appears to be exceptionally bright even though the video showed them scaling the pyramid at night.
The Great Pyramid, also known as the Khufu pyramid, is the largest in Giza, standing at 146 metres (480 feet) tall, and the only surviving structure of the seven wonders of the ancient world.
Climbing pyramids is forbidden in Egypt.
In 2016, a German tourist was barred from entering the country for life after he posted online footage of climbing one of the ancient structures.
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