Aer Lingus chief executive Christoph Mueller said last night the airline is "very, very confident" that the three-week cabin crew roster dispute will be resolved.
Addressing the annual general meeting of the Dublin Chamber of Commerce, he apologised to the business community for the disruption caused.
He spoke as efforts to end the dispute continued with crucial talks at the Labour Relations Commission going into their fourth consecutive day.
Last night sources said the company had submitted a "final" position paper which was being considered by the IMPACT union.
The dispute over a new work roster is now in its third week and has disrupted flights for thousands of passengers.
Aer Lingus began cancelling flights more than two weeks ago after striking staff refused to work the new rosters. More than 300 Impact cabin crew have been taken off the payroll and are going through a disciplinary process that could lead to them being sacked.
Since the dispute began Aer Lingus has been hiring in planes and crews from other airlines to minimise disruption to its schedules but Impact said that staff remain available for work.
Mr Mueller warned that the future of the airline would not be endangered for the sake of a small number of employees.
"We cannot endanger the whole species," said Mr Mueller.
"There are some employees who simply cannot agree to the new conditions. They cannot for a variety of reasons. It has always been my prevailing principle, to respect the individual and to honour the individual needs."
Mr Mueller praised staff for accepting drastic cuts under his ?97m Operation Greenfield cost-saving plan.
"What we have achieved in the last year with our employees and with trade unions was fantastic," he said.