Irish MEPs have written to the EU’s High Representative on Foreign Affairs calling on him to raise their "deep unease" with Russian officials at the highest levels.
Russian warships are making their way towards Ireland, as the Government begins "scenario planning" for economic sanctions being imposed on Moscow.
Nato is monitoring a task group of Russian ships travelling through the Norwegian Sea towards Ireland to participate in a live-fire exercise off the south coast.
A nuclear-powered submarine is among the group of ships due to conduct military drills in the waters 240km from the Cork coastline.
They are expected to begin on Thursday, February 3 and will run for five days.
In a letter to Vice President Josep Borrell, 10 of Ireland's 13 MEPs say the Russian navy's plan has caused "significant worry".
"Mr Borelll, as representatives of the Irish people in the European Parliament, we request that you as the EU's High Representative raise, at the highest levels in the Russian Government, your deep unease at these manoeuvres and request no further manoeuvres take place," the letter states.
The cross-party letter, which was signed by all MEPs apart from Mick Wallace, Clare Daly and Luke Ming Flanagan, acknowledges that international law allows operations of this nature, however, they say that the planned manoeuvres "must be viewed in the current context".
"An operation so close to Ireland at a time of heightened tensions between other EU Member States and the Russian Federation, has caused worry among our citizens and concern in our government."
Reports have suggested that the vessels on their way toward Irish waters are carrying anti-ship missiles and anti-submarine systems.
The exercise is said to be Russia seeking to show Europe that its military is capable of conducting operations on its western sea borders.
Tánaiste Leo Varadkar has said his department is examining the impact of EU sanctions on Russia if they invade Ukraine and any potential counter-sanctions that may be imposed.
His department is profiling how such measures would affect Irish businesses.
He said the experiences of Covid had shown how businesses can be helped through an international crisis.
Mr Varadkar also reiterated that planned Russian naval exercises off the Irish coast are unwelcome and a matter of concern.
Russia is demanding security guarantees from the West, including a promise by Nato never to extend membership to Ukraine.
Nato has made no concessions to the main Russian demands.
Foreign Affairs Minister Simon Coveney, meanwhile, has expressed surprise that a meeting took place between his own Defence Forces chief of staff and the Russian ambassador to Ireland.
Mr Coveney told a meeting of the Fine Gael parliamentary party that he was “surprised, to put it mildly” at Lieutenant General Seán Clancy’s meeting with Yury Filatov.
The meeting heard that Lieutenant General Clancy said the photo-op was part of a round of engagements with diplomats.
Cork North West TD and former minister Michael Creed raised the timing and appropriateness of the meeting.
Mr Creed said the threatened land war between Russia and Ukraine would be like "Syria on steroids".
The former Agriculture Minister has said there now needs to be a debate around Ireland's neutrality and our triple lock system given Russia's plans to carry out manoeuvres in Irish waters.
"This wasn't an application that was made to Ireland that Ireland accepted, this was a notification that we got. They don't have to apply to us for this to happen," he said of the Russian plans, adding that he wishes it was otherwise.
"We can't divorce all of this from the broader global context, which is the Ukrainian crisis. I mean, you have to ask yourself, why is it that, for the first time ever as is my understanding, the Russians would seek to do a military or naval manoeuvre in this area?
The Cork North West TD added that he wouldn't like to see Irish fishermen putting themselves in harm's way.
Mr Creed said he would welcome a discussion on Ireland's neutrality given the rising tensions.
"I think the triple lock is all very well in theory - in other words, a government approval, a Dáil approval and the United Nations approval for actions by the Irish military - but a UN approval requires a unanimous decision by all five permanent members of the Security Council. And therein is the problem for us insofar as it effectively outsources or gives a veto to others on actions that we might take.
"There are many times when we see humanitarian crises developing and say somebody should do something, but we are hamstrung ourselves from doing something if there isn't unanimity in the Security Council on these matters. That's effectively outsourcing or giving a veto to others," he told RTÉ's Today with Claire Byrne show.