Gardaí have launched an investigation after several drones were spotted operating in a no-fly zone off Howth as the Ukrainian president arrived in Dublin earlier this week.
Mr Zelensky landed at Dublin Airport for his first official visit to Ireland shortly before 11pm on Monday night.
Crew on board the Irish naval vessel LÉ William Butler Yeats spotted several unidentified drones north of Dublin around the same time.
RTÉ News understands that the drone activity took place more than 10km off-shore, east of Howth and Dublin Bay.
The LÉ William Butler Yeats' weapons were not used to intercept the drones but it is understood extensive video footage of them was obtained.
An Garda Síochána's Special Detective Unit is investigating the drone sightings.
Gardaí said the SDU will be liaising with the Defence Forces and international security partners.
Senior Government figures, including Taoiseach Micheál Martin, have been briefed on the incident.
The Irish Aviation Authority (IAA) had implemented a no-fly zone for drones over and around Dublin to coincide with Mr Zelensky's visit.
Speaking at the British-Irish Council in Wales, Mr Martin said that there would be a meeting of the National Security Council later this month and the issue would be discussed there.
"Suffice to say that since the onset of the Ukrainian war there's been heightened activity on the cyber security front, in terms of maritime issues and in terms of drones," he said.
Asked if that would suggest that Russia was involved in the drone activity, he responded, "I'm not going to make any comment until we have a full review".
The Taoiseach said that the security operation around Mr Zelensky's visit to Ireland this week went "particularly well".
He added that there will be a review of the security operation and that will encompass drone activity.
Mr Martin noted that drone activity has become a "feature now across Europe".
Earlier, Minister for Defence Helen McEntee said that "everything went according to plan" during Mr Zelensky's visit to Ireland.
Also speaking at the British-Irish Council in Wales, Ms McEntee said that she would not comment on security matters, but said that a significant security operation was in place in order to facilitate a "hugely successful visit".
The minister would not be drawn on whether she was briefed on who was responsible for the drones.
Asked if it highlighted gaps in Ireland's security and defence capabilities ahead of Ireland's assuming the EU Presidency, Minister McEntee said that "everything went according to plan" during Mr Zelensky's visit, adding that there is also a new national development plan which increases funding for the Defence Forces by "more than half".
"I'm committed as minister to making sure that money is spent, that money is invested in our Air Corps, in our Naval services, in our Defence Forces on the ground that are developing our technology, whether it's sonar or radar," added Ms McEntee.
No point in drone-free zone if it cannot be enforced - retired Lt Col
Retired Air Corps Lieutenant Colonel and airport security and safety auditor Kevin Byrne said there is "no point" in having a drone-free zone if it cannot be enforced.
Speaking on RTÉ's Today with David McCullagh programme, he described the situation as "sinister".
"It's remarkably sinister to have four of these, perhaps five, flown from either off the coast or perhaps on land, and having it done by malign actors, who are with us here in the Republic of Ireland, is not good news at all," he said.
"The one thing we do need to do is capture one of these things and see where it came from."
Mr Byrne said incidents such as this should not be taken lying down and would continue to happen "again and again" unless stopped.
