Still images from the footage appeared to show a militant, dressed in black and with his or her face covered, at landmarks in Istanbul popular with tourists.
A voiceover warns that Turkey will become a "target for jihad", threatening a "fiery battle" in a country that has already suffered dozens of Isis-inspired attacks in recent years.
It featured a chant, popular among Isis supporters, threatening to attack the "disbelievers" in their homelands, according to the terror monitoring website Site Intelligence Group.
Among the sites to feature in the footage is the Sultan Ahmed Mosque, also known as the Blue Mosque, one of Istanbul's most famous attractions.
Other images show the suspected Isis supporter standing next to a police car and on a tram in the city.
English language news site The New Arab quoted a narrator in the video as saying: "Oh believers, Turkey has now become a target for your jihad. Seek help from God and attack.
"Make its security shake and its comfort become a state of terror, then turn it into a place of fiery battle."
On Monday night Turkish police captured an Uzbekistan national who authorities said confessed to the massacre at the Reina nightclub that left 39 people dead.
Abdulgadir Masharipov was reportedly found along with his four-year-old son during a raid on a home in an Istanbul suburb.
Turkish Prime Minister Binali Yildirim announced that the "vile terrorist who attacked the place of entertainment on New Year's Eve and led to the loss of so many lives has been captured".
He can be held for up to 30 days under Turkey's state of emergency, which was introduced after a failed coup attempt in July, before he is charged and formally arrested.
Isis claimed responsibility for the New Year's attack, saying it was in response to Turkey's military action in Syria.
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