"We would like to sincerely apologise for the inconvenience caused", the airline said.
Boeing reiterated on Sunday it was working with global regulators to certify a software update for the jet as well as related training and education material to safely return the plane to service.
Cork Airport managing director Niall MacCarthy said he regretted the grounding of Norwegian's aircraft.
Boeing is not expected to submit its formal software fix to the FAA this week or conduct a certification test flight that is required before it can submit the fix and training upgrade for approval, two people briefed on the matter told Reuters.
Once the FAA approves the MAX for flight, Southwest has said it would take about 30 days to get the jets up and running again.
The Chicago-based planemaker faces an estimated $1.4 billion bill for canceled flights and lost operating profit at airlines if the Max is still grounded by the end of September, said Bloomberg Intelligence analyst George Ferguson.
"No one should take that as some indication that we don't think the aircraft will be ready by August 19", Parker said during the company's annual shareholders meeting.
Boeing Co.'s 737 Max aircraft, grounded since March after two fatal crashes in five months, should be back in the air by December, a top U.S. regulator said.
Still, Parker said he understood there is "an absolute fix" for the 737 Max that will make it safe, while acknowledging it may take time to regain public confidence in the aircraft.
Hailu said the airline will only fly the aircraft after it had been certified and flown by American and European airlines, adding that Boeing would have to also train its pilots on the technicalities of the aircraft.
Shares in Delta, which does not operate the MAX, have outperformed those of US rivals with the jets.