Police called in Army Technical Officers from Palace Barracks to examine the items found on Saturday night at Forest Street in the Clonard district.
A number of local residents were evacuated from their homes for their own safety overnight while the security operation was completed.
A 52-year-old man was arrested and is being questioned about the bomb parts and weapons find.
Det Sgt Kenneth Leckey of Tennent Street CID said: “Firearms and ammunition were discovered by police at a house in Forest Street last night, Saturday 24 January.”
DS Leckey said Cavendish Street Hall was made available for residents who had to leave their homes while the items were made safe for removal to be forensically examined.