The Government is inviting the two sides in the Aer Lingus cabin crew roster row to attend the Labour Relations Commission.
The talks to resolve the dispute broke down on Friday evening, following three days of negotiations, between management and IMPACT officials.
The Transport Minister said he is concerned about the prospect of two further days of strike action at the airline next week.
"If the union and the company can't resolve the situation by bilateral talks, they should now go to the Labour Relations Commission … they will try and broker a compromise," Varadkar said.
"What's happening at the moment is megaphone diplomacy - and that isn't serving anyone's purpose."
The continuing dispute centres around rosters for cabin crew, who are seeking a five-days-on, three-days-off pattern, which is currently used for pilots.