Yoon Young-Doo, who made the comments as he prepared to fly to the United States to meet with transportation safety officials and victims, also told reporters in Seoul: "I feel tremendous responsibility for those affected by the crash."
He added that the airline would boost its landing simulation training for pilots.
Yesterday, the boss of South Korea's second-largest airline lashed out at media reports that pilot inexperience may have been to blame for the fatal crash, calling it "intolerable".
The trainer, Lee Jung-Min, had received his teaching licence for the Boeing 777 just a month before the crash on Saturday, although he is an experienced pilot with thousands of flying hours, Asiana said.
He was assigned to guide colleague Lee Kang-Kuk, who was landing in the US city for the first time on that model of aircraft.
Two teenage Chinese girls were killed and more than 180 people injured when the flight from Seoul clipped a seawall short of the runway and went skidding out of control on its belly, shredding the tail end of the plane and starting a fire.
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