They were called to reports of a man with a firearm on the Links close to St Mary's primary school at around 8.15am today (Monday).
Police were keen to reinsure members of the public that at no point was there any risk to the public, and it is understood the firearm was a soft pellet gun.
A Police Scotland spokeswoman said: “Police in Edinburgh can confirm that a 24-year-old man has been arrested following the recovery of a weapon at Leith Links.
“The incident was reported to police around 8.15am on Monday, April 29, following reports of a man with a firearm.
“Armed officers responded and the man was quickly arrested and taken in to custody. At no point was there any risk to the public.
“Officers are continuing to investigate the full circumstances. Anyone with information can contact Police Scotland on 101.”
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