The Federal Aviation Administration on Wednesday issued new orders requiring that air traffic control supervisors oversee the arrival and departure of planes carrying the vice president and first lady.

The directive came two days after an incident in which a Boeing 737 carrying Michelle Obama got too close to a massive military cargo jet as both planes were trying to land at Andrews Air Force Base.

The managers in one air traffic control center were unaware of a potential problem, and the manager in the Andrews tower was reluctant to say anything when he noticed that the two planes were two miles closer than FAA standards allow, federal sources said.

Oversight by a manager already is required when the president is on board a White House aircraft.

In a statement Tuesday, the FAA said that “the aircraft were never in any danger.”

The National Transportation Safety Board, which began investigating mistakes by air traffic controllers and pilots last year after error rates spiked, said Wednesday that it will investigate the incident.

An FAA investigation, already underway, is expected to be completed next week.

On Wednesday, the NTSB said it had reviewed 950 cases in the past year when cockpit collision-avoidance systems were triggered, 260 of them worthy of further examination and nine that warranted full investigations.

The worst was an incident last year when, because of a controller’s mistake, a US Airways plane passed within 50 feet of a cargo jet in a cloud bank after taking off from Minneapolis, said Thomas E. Haueter, director of the agency’s Office of Aviation Safety.

“The one in Minneapolis scares the heck out of me,” Haueter said. “That’s the one we lose the most sleep over.”

Ninety people were on board that Philadelphia-bound flight. The cargo plane’s pilot said he never saw the Boeing 737.

Haueter said a near collision in January between an American Airlines Boeing 777 and two C-17 military cargo jets just south of New York also ranked as one of the most serious incidents.

The NTSB, better known for its investigation of plane crashes, intensified its review of nonfatal incidents a year ago to determine whether an apparent increase in the number of errors by air traffic controllers and pilots was evidence of a systemic problem.

They required airlines or pilots to file reports directly to the NTSB whenever collision avoidance systems aboard aircraft went off.

Haueter said the data have not revealed a pattern.

“Usually a problem was caused when somebody made an assumption, like assuming that somebody was going to turn right, and then they didn’t,” he said. “The big issue is that it’s just the first year we’ve been looking into this. It’s probably going to take three to four years to get a better idea of what’s going on.”

On Monday, Obama and Jill Biden, the wife of the vice president, were returning from a television appearance and other events in New York aboard a Boeing 737 that is part of the White House fleet of aircraft.

As the incident unfolded just before 5 p.m., the managers at the Potomac Terminal Radar Approach Control (TRACON) facility in Warrenton were occupied with other duties and unaware that one of their controllers had allowed the first lady’s plane to get two miles closer than allowed by FAA regulations to the wake of a 200-ton C-17, federal sources said.

“Normally, when the president’s plane comes in, a manager is stationed right over the controller’s shoulder,” said an FAA official who spent years working in Washington area control facilities.

Although the Warrenton managers were unaware of what was happening, the manager in the tower at Andrews — now known as Joint Base Andrews — was watching it unfold on a radar screen, federal sources said.

But that manager was reluctant to contact the Warrenton center and “tell them what to do,” according to a federal source familiar with the investigation who asked not to be identified because he was not authorized to speak publicly. The Warrenton controller’s error was rated an “A,” the top of the FAA scale for degree of seriousness.

The first lady’s jet ended up making a “go-around,” a routine safety maneuver, because the Andrews controllers concluded that the C-17 might not be able to clear the runway before the White House plane landed.

Wake turbulence from the C-17, which ripples behind planes like waves in the wake of a supertanker ship, was a potential danger. It is powerful enough to severely buffet a trailing plane and, in extreme cases, result in a crash.

Potomac TRACON controllers, who are responsible for planes using airports throughout the region, recorded 52 controller errors last year, an increase from 21 in 2009. This year, the facility has recorded 13 errors. At least two other errors rated a “B” in degree of seriousness have occurred there this month.

Last Thursday, a single-engine, four-seat plane bound for the Leesburg airport came within a mile and 200 feet of altitude of another small plane leaving the Manassas airport. General FAA rules require separation of three miles and 1,000 feet in altitude.

On Sunday, a single-engine Cessna circling Reagan National Airport flew into the flight path of an arriving Delta Boeing 757, coming within half a mile and 700 feet of altitude.

On Wednesday, Transportation Secretary Ray LaHood said on “PBS NewsHour” that he had fired two controllers — one in Knoxville, the other in Miami — who had been caught sleeping on the job recently.