The Irish Aviation Authority (IAA) says it will allow flights to resume from all Irish airports but volcanic ash could bring more disruptions later in the week and periodically throughout the summer.
The IAA had closed airports for six hours on Tuesday due to a risk of ash ingestion in aircraft engines, although overflights of Ireland from Britain and continental Europe had not been banned.
"The situation will be reviewed as the week goes on," the IAA said in a statement.
Continued northerly winds forecast for the coming days could bring more clouds of volcanic ash from an Icelandic eruption and disruption for passengers this week, it said.
"We could be faced with this periodically during the summer," IAA chief executive Eamonn Brennan told public radio station RTE.
"We are probably facing a summer of uncertainty due to this ash cloud."
Earlier on Tuesday former state airline Aer Lingus said last month's closures lasting several days cut its earnings by about 20 million euros ($29 million), with the final bill dependent on the impact on passengers' longer-term travel plans.