British Airways CEO Alex Cruz has asked the pilots' union to sit down with management and attempt to resolve the dispute.
He added that he wants to settle the dispute as soon as possible.
"The commitment of everyone at British Airways is to get over this particular dispute as quickly as possible and we urge the union to sit down with us as quickly as we can so we can reach an agreement," he said.
On August 23, the British Airline Pilots Association (BALPA) announced that it called on its members to strike from 9-10 September, and on 27 September, following disputes over pay and perks cuts.
The company called on the passengers to stay home if their flight has been canceled.