Ireland's pharmaceutical industry has said there are always two to three months' supply of medicines in the system and these stocks will help absorb any short-term delays that could arise from a disorderly Brexit.
The Irish Pharmaceutical Healthcare Association said the advice to patients is "not to panic".
It repeated its previous advice that there is no need for patients, or pharmacists, to stockpile medicines.
The association said it is satisfied that arrangements are in place to mitigate against a shortage of medicines, in the event of a disorderly Brexit.
IPHA said that in some cases, companies are re-routing transport away from the UK, to mitigate against problems with the supply chain.
The organisation said that Irish authorities have been working closely with the pharmaceutical industry on detailed scenario-planning.
It said there is no need for hospitals, pharmacists or patients to order extra quantities of medicines, or for doctors to issue extra prescriptions.
The Irish Pharmacy Union said pharmacists were naturally very concerned about medicine supplies for patients and so it is in constant contact with health authorities and wholesalers and manufacturers to plan for any problems that might happen.
"We have been told that everything that can be done is being done to plan for and prevent any potential problems that could crop up", the union said.
The IPU said it was still advising pharmacy members that they do not need to stockpile extra medicines.
It said it had been assured that none of the shortages that currently exist are directly attributable to Brexit.
The Department of Health said that significant work had been undertaken, in so far as possible, to anticipate potential vulnerabilities in medicine supplies after Brexit.
It said that Brexit may cause those with a small share of a particular medicine market, to consider the ongoing viability of supply to Ireland.
But it added that any products that may be affected would be unlikely to be critical to continuity of care as there and and will be alternative suppliers, or therapeutic alternatives available.
The department said that there are already extra stocks of medicines routinely built into the Irish supply chain and that Ireland's medicines supply model is different to what operates in the UK.
It said that the pharmaceutical industry and wholesalers have provided assurance that they are confident they will have sufficient stocks, to bridge any initial issues at ports, should they occur.
The department said that similar work has been underway to protect the medical devices area, which covers a wide range of products from sticking plasters and bandages, to more complex equipment like hip implants and coronary pacemakers.
In relation to continuity of health services, the department said that the Irish and British governments have committed to the shared objective of maintaining the Common Travel Area (CTA) arrangements, which have allowed Irish and UK residents to access health services, in each other's jurisdictions.
This will include maintaining current arrangements for access to routine, planned and emergency health services for UK/Irish residents and visitors in the other jurisdiction.
It also includes health cooperation on access to specialist health services in the other jurisdiction, for example on an all-Island basis, for paediatric cardiology and cancer care.
Following Brexit, EU regulations will no longer apply to the UK.
It looks likely to result in an end to the EU Cross Border Directive system, whereby patients from the Republic of Ireland can get operations in another EU member State and be reimbursed afterwards for the cost by the Health Service Executive.
While there remains much uncertainty over what will exactly transpire, it may mean patients no longer being able to have operations in Northern Ireland, or the UK but they would continue to have access to care in another EU country under the EU scheme.
