Police are appealing for information after the incident which took place at Fort Kinnaird on Thursday, June 3.
Around 5pm, four men were approached by two men who were on a motorcycle.
A short chase then took place, and one of the men was stopped on Whitehill Road when the pillion passenger on the bike assaulted him with a bladed weapon.
The two suspects then made off along Whitehill Road.
The 31-year-old victim was taken to the Royal Infirmary of Edinburgh with serious injuries, where he remains in a critical but stable condition.
The driver of the bike was dressed in all black clothing with a black helmet.
The passenger was wearing a jacket with a red body and grey sleeves, with a dark cap and a snood/ dark face covering.
They were riding on an off road/trials/scrambler bike which was mainly blue in colour, with red and white livery.
Detective Inspector Clark Martin from Gayfield CID said: “We believe this incident was targeted towards the group of men standing at Fort Kinnaird and the victim has been left with extremely serious injuries.
“I am appealing for anyone who witnessed what happened, or noticed the suspects in the area, to please come forward.
“The motorcycle they were using was very distinctive and I would also urge anyone who thinks they may have seen it in the Edinburgh area on Thursday to pass this information on to the police.
“Anyone with information is asked to contact Police Scotland through 101, quoting incident number 2632 of Thursday, 3 June.”