Two Ministry of Defence bomb disposal experts attended the latest incident at flats yesterday before carrying out a controlled explosion on the suspicious material on nearby Leith Links.
It follows an evacuation from Fidra Court, a high-rise tower block in Muirhouse, on April 18 following the alleged discovery of suspicious items.
A 61-year-old man has appeared in court in connection with the earlier incident, which resulted in hundreds of people being temporarily moved to a leisure centre.
Yesterday a number of properties in the city's Persevere Court were searched and a wide area around them was cordoned of.
A number of police riot vans were on the scene with the much of the surrounding roads cordoned off for around six hours.
The Ministry of Defence confirmed a two-person bomb disposal unit had been working alongside the police.
Police said the incident affected only Persevere Court.
There have been no arrests in connection with the incident.