A group of people who were with the boy raised the alarm at around 5.10pm.
Police were assisted over the weekend by coastguard teams from Aberdeen, Arbroath, Montrose and Stonehaven, along with a fire service water rescue unit.
Police confirmed on Monday morning they are continuing searches in the area.
However, the coastguard says it has not rejoined the search.
A Police Scotland spokesperson said: “Police were made aware of a 15-year-old boy in difficulty in the water in the River North Esk near Gannochy Bridge, Edzell, around 5.10pm on Saturday.
“Emergency services remain in attendance and searches are ongoing.
“The boy’s next of kin are aware.”
Search for 15-year-old boy swept away in river near Edzell enters third day