"We shouldn't have been in this process. The case brought by BA was trivial," he said.
BA said in a statement it was "very disappointed", adding that it would implement a contingency plan to keep planes flying.
It intends to fly more than 70 per cent of the customers booked to fly.
Originally the union had planned to stage strikes from May 18-22 , May 24-28 , May 30-June 3, and June 5-9.
The dispute with cabin crew over pay and conditions had already resulted in seven days of strikes in March, which cost the airline $64.56m.
The airline and Unite have been locked in a bitter battle over pay and conditions for months as BA attempts to cut costs.
While the two have reached broad agreement on pay, the sticking point is now the heavily discounted flights available to cabin crew - key perks which BA has taken away from workers who have gone on strike.