Aer Lingus will negotiate with unions about staff cuts of up to 900 jobs at the airline.
It comes as Ryanair announced up to 3,000 jobs across pilots and cabin crew could be cut "as a direct result of the unprecedented Covid-19 crisis".
An Aer Lingus spokesman said: "Aer Lingus is continuing to communicate directly with our employees and engage with their representative bodies."
Labour TD Duncan Smith has called on Aer Lingus to do everything it can to retain jobs and for urgent government intervention. "The news that Aer Lingus are in talks with unions to cut over 900 jobs at the company is extremely concerning. This follows speculation from Ryanair that job losses of over 3,000 people could also happen in the next year," he said.
"The overall goal here has to be to retain as many jobs as possible. We are a small open economy, we need a vibrant aviation sector to help encourage trade and tourism.
"My thoughts today are with the workers who face uncertainty. The Government needs to extend the temporary wage subsidy scheme for industries that are going to be key for getting us back on track such as Aer Lingus.
"It is clear that the government need to take urgent action to address the potential torrent of job losses that could occur at Dublin Airport between Aer Lingus and Ryanair."
Ryanair chief executive Michael O'Leary, whose pay was cut by 50% for April and May, has agreed to extend the reduction for the remainder of the financial year to March 2021.
Ryanair said its flights will remain grounded until "at least July".