But officers are convinced that the crucial clues they need to solve the crimes will come from closer to home.
Detective Superintendent David Gordon said: “This is now a major investigation led by the Organised Crime Unit, reflecting how serious we are taking these reckless and dangerous acts.
“We need information from the public about who committed these offences and the current location of the firearms used in these crimes. We believe the answer lies within the local community and are appealing for anyone who has information, to come forward.”
Firearms incidents in Gilmerton over the weekend are now being linked to another shooting at a house in Fernieside Avenue a fortnight ago.
A Range Rover belonging to Dionne Hendry, the wife of killer Jamie Bain, was shot at on Saturday, while a homemade bomb wrapped in a Liverpool FC scarf was placed on the doorstep of the home she shares with two others in The Murrays Brae.
Another device was put outside a house in Walter Scott Avenue, at around the same time shots were fired at a property in Gilmerton Dykes Drive.
Neither of the bombs were active but both carried threatening messages, including the note: “Pay what you are due lad.”
The incidents have sparked fears of an ongoing gangland feud, and police are working with forces across the UK on the case.
The Organised Crime Unit has now launched a single investigation into the four incidents, plus an additional report of suspicious activity outside a property in the Hyvots Bank area on Friday.
Det Supt Gordon said: “We are in liaison with a number of UK police forces and we are looking at all possible intelligence and information that suggests the involvement of any other individuals throughout the UK.”
It is not clear how many people were involved in Saturday’s events, but officers are keen to get more information about two people seen on a motorbike in The Murrays at around 9.30pm.
Det Supt Gordon said: “The rider had a helmet, but it is unclear if the passenger was wearing a helmet or had a hood over the head. Police Scotland are doing everything within their capabilities to ensure that the threat does not escalate. We have significant resource in the area to reassure the public and there is a significant police investigation.”
The Fernieside Avenue home, occupied by two people, was sprayed with bullets by someone in a hooded top at around 12.40am on September 9. Police are still looking for a dark blue coupe getaway car – believed to be a Seat Leon – which was driven off by a second person.
Police said Friday night’s suspicious incident at Hyvots Bank Avenue – at which two men arrived at a house and asked for a particular individual between 9.30pm and 9.45pm – was also crucial. The first man is described as white, in his early 20s, 5ft 10in tall, of medium to slim build and wearing a grey jogging suit. The second man is described as white with dark hair. Police are also reviewing reports that several doors on the same street were covered with lighter fluid earlier this year.
The devices found on Saturday are thought to have been left by Liverpool gangsters to whom Bain – currently serving a life sentence for the murder of former boxing champ Alex McKinnon at the Marmion pub in 2006 – is said to owe money.
Chief Inspector Richard Horan said: “We have high visibility police patrols in the area to offer community reassurance and we will be delivering leaflets door to door in the area over the coming days.”