The agency is currently based at Canary Wharf in London
The Health Minister Simon Harris says Dublin should become the new home for the European Medicines Agency (EMA).
He told an industry gathering in the city that it would be "a fantastic" base for the agency.
Speaking at the Irish Pharmaceutical Healthcare Associations (IPHA) annual dinner, he called on delegates to support Ireland's bid.
The agency is currently based at Canary Wharf in London.
Minister Harris highlighted the vital role the EMA plays in protecting public and animal health by ensuring that all medicines available on the EU market are safe.
He also spoke about the importance of minimising disruption to the EMA and its employees post-Brexit.
"Dublin would be a fantastic new home for the EMA and we would very much welcome your support in bringing this key agency to Dublin", he told delegates.
"Given the proximity to its current home in London and as English is the working language of the EMA, a move to Dublin would ensure any disruption to the agency’s vital work and employees would be kept to a minimum.
"Ireland has a proactive and highly regarded national medicines agency in the shape of the HPRA.
"In addition, as a modern capital city Dublin has much to offer as a home for such a vital organisation with excellent air connectivity, a strong pharmaceutical sector and an excellent research community."
The agency is responsible for the scientific evaluation, supervision and safety monitoring of medicines developed by pharmaceutical companies for use in the EU.