UPDATE 1-Airline profits could feel squeeze from Tropical Storm Harvey

(Adds details, Airlines for America comment)

NEW YORK, Aug 29 (Reuters) - Tropical Storm Harvey has already caused thousands of flight cancellations around Houston and could cripple regional aviation through the U.S. Labor Day holiday, taking a bite out of airline profits during one of the year's busiest travel periods.

Since making landfall on Friday, the deadly storm has dumped several feet of rain on Houston and surrounding areas, forcing the temporary closure of three airports.

Normal regional airline operations will likely not resume until Wednesday or Thursday, even under the best-case scenario.

The Houston airport authority has not said when it will reopen, but the Federal Aviation Administration said it would not be before Wednesday for Hobby Airport and Thursday for Houston Intercontinental Airport.

Conditions might put off normal service through the close of the Labor Day travel period, which had been projected to be even busier than normal this year.

The exact financial impact was not yet known, but even minor storms can cost airlines millions of dollars. A late winter storm earlier this year forced Delta Air Lines Inc to cancel thousands of flights, resulting in a $125 million negative impact.

Since Sunday, airlines have canceled more than 5,000 flights into and out of Houston, including all scheduled flights through Wednesday, according to the air travel monitoring website flighware.com.

After airports reopen, it will likely be at least several days before full operations are possible, experts said.

"There is no question that the devastation affecting one of the largest metropolitan centers in the United States and a major air travel hub, as well as outlying areas and other cities in the region, will curtail the passenger volumes previously projected for this period," said John Heimlich, vice president and chief economist of trade group Airlines for America.

Southwest Airlines Co, one of the region's largest carriers, said it was possible the storm could prohibit normal flight schedules at Houston Intercontinental and New Orleans International airports through Sept. 5.

The seven-day Labor Day travel period stretches from Wednesday, Aug. 30 through Tuesday, Sept. 5.

United Airlines, which has a major hub operation in Houston, has canceled about 2,000 flights through Thursday.

(Reporting by Alana Wise and David Shepardson; Editing by David Gregorio and Meredith Mazzilli)