There was smoke but no fire Tuesday at a vital air-traffic center tucked away in an Elgin office park, but its evacuation left thousands of passengers in Chicago and across the country waiting hours for flight stoppages to be lifted at the city’s two airports.

The catch-up process continued into the evening, even after the airlines serving O’Hare International Airport canceled more than 1,000 flights and operated more than 1,200 flights late, according to FlightStats.com.

“Some of those cancellations were proactive to allow the airport to recover,’’ said United Airlines spokeswoman Christen David.

The disruptions followed a rough travel day Monday, when more than 500 O’Hare flights were cancelled and more than 1,200 flights delayed due to severe thunderstorms sweeping across much of the U.S.

At Midway Airport on Tuesday, airlines canceled more than 120 flights and more than 260 flights were delayed, according to airline monitoring by FlightStats.com.

Passengers planning to fly out of Chicago on Wednesday should check with their airline before heading out, officials advised. Some airlines were temporarily waiving the fees normally charged to rebook on different flights.

Tuesday’s problem at the federal Terminal Radar Approach Control, or TRACON, facility in Elgin, which directs all commercial flights approaching and departing the Chicago area, was traced to a faulty motor that controls fans in the bathrooms of the building, fire officials said.

It caused an acrid smoke that required a full-scale evacuation around 11:30 a.m. of the roughly 50 air-traffic controllers and other staff who are normally in the building during the day, Federal Aviation Administration officials said.

“The incident itself was not a huge deal,’’ said Elgin Fire Capt. Robb Cagann, adding that at no time was there a fire.

But the impact was felt at airports across the country, officials said, because the shutdown of the radar facility triggered a complete ground stop at O’Hare, Midway and on flights destined for Chicago.

It meant that for more than three hours — during the busy travel period that air-traffic controllers call “the noon balloon’’ — no planes were allowed to take off from O’Hare or Midway. Chicago-bound planes still on the ground in other cities were held for departure.

An undetermined number of Chicago-bound flights that were already in the air had to be diverted to other airports to wait out the ground stop, the FAA said.

Cellphones started ringing as frustrated passengers on diverted flights or on planes that had pulled back from gates and were parked on the airfield called friends and relatives, asking what they had heard and relaying stories about exiting their planes, reboarding and exiting again.

“We’re on the plane again for the third time,’’ United Airlines passenger Dan Farris emailed to the Tribune shortly before 3 p.m. His flight from O’Hare to Phoenix was originally scheduled to depart at noon, and a revised 2 p.m. departure time did not happen, either, he said.

“The terminal was packed the first time out and now it’s not crowded at all,’’ Farris said after boarding the plane for the third time, which turned out to be the charm.

After the evacuation of the TRACON facility, six controllers who work at the facility drove to Aurora, where the FAA operates Chicago Center, a radar facility that normally handles planes at high altitude that are traversing the Chicago-area airspace en route elsewhere, said Doug Church, a union spokesman for the National Air Traffic Controllers Association. The six controllers handled some of the first planes taking to the air and arriving in the Chicago area after being diverted to other airports, Church said.

The all-clear was given at the TRACON site around 2:45 p.m., but it took hours for flight activity to ramp back up, officials said.

A Tribune reporter counted more than 100 passengers waiting patiently in line at the American Airlines ticket counter at O’Hare, while others filled chairs and sat on the floor of the busy airport.

Astrid Henry, 47, a college professor who lives near Des Moines, said the daylong ordeal she had endured at O'Hare was “horrific” and “freakishly weird.”

“It's just so random that these things would happen back to back,” she said, referring to the storm that likely halted her plane out of Chicago Monday night, and the ground stop that left her still stuck here Tuesday afternoon.

Henry and her partner landed at O'Hare on Monday evening on a flight from Copenhagen, Denmark, expecting to connect to Des Moines later that night. But the Iowa-bound flight was cancelled, presumably because of the rainstorm that passed through the Chicago area, she said.

After many confusing encounters with airline personnel, the couple were eventually booked on separate flights home. Henry’s partner was confirmed on a noon flight Tuesday to Des Moines, while Henry was confirmed on a 2 p.m. Tuesday flight to Cedar Rapids.

Even landing at separate airports, the couple were just eager to get home.

But at 4 p.m. they were still at O’Hare, their flights cancelled. But, they were told, their luggage had made it to Des Moines.

“Luckily we put toothbrushes in there,” Henry said, pointing to a small carry-on bag.

Although they were given confirmed seats for a flight Wednesday, the couple decided to rent a car and drive home instead.

For Jean Henderson, the ordeal capped off an otherwise “wonderful trip” to Europe, where she and her husband had visited their daughter.

The couple’s flight from London landed at O’Hare at 10 a.m. They were supposed to board a Cleveland-bound American flight scheduled to leave O’Hare at 2:05 p.m., Henderson said. But they learned 10 minutes before their flight was scheduled to depart that it had been cancelled, and that they would have to wait until Thursday for a direct flight to Cleveland, where they live, Henderson said.