They were posted with Irish stamps and had Dublin as the return address, prompting gardaí to join the investigation.
They are also investigating claims that the "IRA" is responsible for the explosive devices.
In January a group calling itself the "New IRA" claimed responsibility for a vehicle bomb outside the courthouse in the Northern Irish city of Derry/Londonderry.
An Garda Síochána have said they continue to liaise with the United Kingdom authorities in relation to these investigations.
But dissident splinter groups have sought to continue their campaign.
Police Scotland said a controlled explosion was carried out as a precaution on a suspicious package found in the mailroom at Glasgow University, after several buildings had been evacuated. One sent to the The Compass Centre in Hounslow in London partially ignited after being opened by staff.More news: Study claims AT&T's fake 5G is slower than other carrier's regular 4G
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"It will obviously go through all the relevant tests".
Mr Flanagan said the item found in Limerick could be the fifth, adding: "We have reason to believe this could be the case".
The Irish police, the Garda, called military bomb disposal experts after the package was discovered Friday morning.
The package - confirmed to contain explosives - had love heart stamps similar to the ones used on letter bombs sent out to universities and stations in the UK.
A DEFENCE Forces Explosive Ordinance Disposal team has arrived at the An Post sorting depot in Limerick where a suspicious package was discovered this Friday morning.
"This is a despicable act", he told RTE.