The Federal Aviation Administration’s chief operating officer stepped down following a string of reports of air-traffic controllers falling asleep on the job.

Henry Krakowski, a former head of flight operations for United Airlines, resigned after meeting with FAA Administrator Randy Babbitt, the agency said in a statement today. Krakowski was in charge of controllers at the agency. David Grizzle, the FAA’s chief counsel, will take the job as the agency seeks a replacement.

“Over the last few weeks we have seen examples of unprofessional conduct on the part of a few individuals that have rightly caused the traveling public to question our ability to ensure their safety,” Babbitt said in the statement. “This conduct must stop immediately.”

The FAA said yesterday two more controllers were caught sleeping on the job, bringing to four the number the agency has reported this year. That number may grow. Two controllers were suspended for failing to hand off control of a departing plane in Lubbock, Texas, on March 29 and for failing to respond until contact attempts were repeated, the FAA said yesterday.

Krakowski was named to his FAA post in 2007, and was only the second person to fill the job Congress created in 2000.