Police have confirmed they were called at around 8.15am to an incident on Leith Links which happened close to St Mary's primary school.
Eyewitnesses have reported the man was holding the gun to his own head when armed police arrived at the scene.
It is understood the weapon involved was a soft pellet gun, which is not classed as a firearm, though police sources said seen from a distance it would look like a gun and could alarm people.
One eyewitness said on Twitter; "Walking the boy to school over Leith Links and suddenly loads of armed police swarming everywhere and heading for a guy on a park bench. "
More to follow