Police said it was discovered at Maeve House in the New Lodge area on Monday after a report from a member of the public.
Army bomb disposal experts were called to the scene and the suspected explosives taken away.
The explosives are said to be enough to make three under-car booby-trap bombs.
Det Insp Stuart Griffin said considerable inconvenience had been caused to residents and he thanked them for their co-operation.
"Thankfully these suspected explosives are no longer in the public domain," he added.
The find comes two years after a similar discovery at Maeve House.
Two and a half kilos of the explosive was found in a cupboard at the building in May 2014.
Speaking about the latest seizure, Deputy First Minister Martin McGuinness said he was "hugely relieved and delighted that these explosives have been recovered and made safe".
"I'm disappointed but not surprised that there are still people within our society who believe that they have the right to attempt to point us all back to the past through attempts to kill people," he told the BBC's Good Morning Ulster.
One and a half kilograms of what is believed to be Semtex plastic explosive have been found at a block of flats in north Belfast.