Met Éireann forecasts predict that Ireland should have minimal disruption due to the volcanic ash cloud over the coming week.
Airports in the west of Ireland have reopened after a weekend of travel disruption.
The Irish Aviation Authority confirmed that all restrictions in Irish airspace have now been lifted, as winds push the volcanic ash cloud from Iceland out over the Atlantic.
The IAA said it expects all airports to stay open until at least 6pm tomorrow.
Met Éireann said that even though the plume remains close to Ireland, current forecasts predict that Ireland should have minimal disruption over the coming week.
European air traffic agency Eurocontrol said today that areas of higher ash concentration could move from over the Atlantic Ocean back toward the Iberian peninsula, threatening fresh airspace closures in Portugal and Spain.
Speaking on RTÉ's Morning Ireland, IAA Director of Safety Regulation Kevin Humphreys said the plume still extends from Greenland down into the Iberian Peninsula, around into the Azores and back into Europe.
He advised intending passengers to check with their airline for flight schedules, particularly those on transatlantic flights.
Airspace restrictions in Portugal have delayed the return of Irish troops from Chad. They are due into Dublin Airport at 2.30am tomorrow morning.
Ryanair says it is adding extra flights to the Canary Islands, following the disruption in service to some southern European destinations over the weekend.
Elsewhere, Minister for Tourism Mary Hanafin is to meet representatives of the tourism industry today to review the effects of the crisis.
It is also hoped they can begin devising a code of conduct to ensure visitors stranded here are properly looked after.
The Government Taskforce on Emergency Planning met this morning to discuss the crisis.
The Environmental Protection Agency has reported no evidence of deterioration in air or water quality levels as a result of the ash.
Meanwhile, Ryanair has confirmed that traces of volcanic ash have been found in the engines of two of its aircraft at George Best Belfast City Airport.
Four Ryanair flights to England were cancelled at the airport yesterday, leaving dozens of passengers stranded.
Initially, the airline said the planes all had separate technical problems unrelated to the volcano eruption in Iceland.
But after further tests the airline has confirmed that two of the aircraft which overnighted at Belfast City airport showed small traces of ash in their engines.
Ryanair said the planes would return to service later today, once the manufacturer's approved procedures have been completed by the airline's engineers.
