The incidents were part of a recurring pattern of fatigue for controllers at O'Hare, where officials were urged to "emphasize the importance of sleep management" in a letter from National Transportation Safety Board to the Federal Aviation Administration.
NTSB aviation safety director John Clark sent the May 16 letter to Russell Chew, FAA's chief operating officer.
On March 21, a Lufthansa plane and a Delta jet were mistakenly instructed to take off at the same time on crisscrossing runways. The planes came within 100 feet before the pilots were alerted and stopped.
The controller was in training and had an untreated sleep disorder, authorities said.
Two days later, planes from United Airlines and its low-cost carrier, Ted, came within 600 feet of each other when one plane was sent to taxi across a runway where the other had started its takeoff roll.
That controller had just four hours of sleep, and told NTSB investigators that he "was not as sharp as [he] could have been," the letter said.
The FAA found that both incidents were caused by controller errors.
"All I can say today is that we will analyze the issues that the NTSB team brought up in their report and consider the recommendations that they have made," FAA spokesman Tony Molinaro said.
A union official defended the controllers, saying they know when they are too tired to work.
"People will occasionally call in sick if they don't get a good night's sleep because they don't want to be put in a bad position," said Craig Burzych, president of the National Air Traffic Controllers Association at O'Hare tower.