Taoiseach Leo Varadkar says he wants people to be able to travel abroad for work or leisure "before the end of the year, if not this summer".
He said Ireland will also need to work with the UK and the EU to manage issues around airports as the coronavirus restrictions begin to be eased.
It comes amid calls for tougher laws to require people arriving into the country to tell authorities where they will be self-isolating.
At the moment, people arriving at Irish airports are required to sign a passenger location form - including details of where they will be staying.
However, Department of Justice figures released this week revealed that more than a third of passengers arriving into Dublin Airport over a six-day period did not fill out the form.
Over 600 people either failed to put in an address or put in something that was too vague for authorities to be able to locate them.
Speaking on The Pat Kenny Show, Mr Varadkar said the Government is working on legislation and regulations to 'underpin' the rules at the country's airports and ports.
He said: “We do keep track of everyone coming through the airport - we have that from the passenger records, for example.
"Almost everyone - the vast, vast majority coming through - are Irish citizens returning home... they’re essential workers.
"If there are people coming here for leisure or tourist visits, those numbers are minimal."
The Taoiseach said that there is no evidence people arriving here in the last few weeks have 'imported' coronavirus into the country, but that the possibility remains a concern.
He also said that concerns around airports will increase as the current restrictions begin to be eased in Ireland and around the world.
He explained: “What we really need is an Irish-British solution within the common travel area, or a European-wide decision on what we do within our airports.
"We want air travel to resume again - I still want the possibility of people to engage in business and leisure travel before the end of the year, if not this summer.
"Some work is being done at European Commission level to make sure we all do the same thing at our airports."
Additional reporting by Michael Staines