(CNN) The only flights into storm-ravaged Houston right now are carrying much-needed supplies.
United Airlines, Southwest Airlines, Spirit Airlines and American Airlines each say they've airlifted supplies into or people out of the city since Hurricane Harvey hit on Friday.
With those limited exceptions, Houston's two airports remained closed to passenger air travel. On Tuesday afternoon, the Federal Aviation Administration issued flight restrictions over the greater Houston area. Those restrictions cover 1,200 square nautical miles over the city and are intended to keep airspace clear for search and rescue flights, the FAA said.
Houston has two airports. George Bush Intercontinental Airport (IAH) is a major hub for United Airlines, and services 28 other airlines and 42 million passengers annually. The other, William P. Hobby Airport (HOU), is a key airport for Texas-based Southwest Airlines and handles 13 million passengers every year.
Flights "are limited to humanitarian flights and first responder support for Hurricane recovery," Houston Airports said Monday.
The closed airports are being used as a staging and re-fueling area for the search and rescue aircraft currently flying about Houston.
United said it would fly two 777 jets loaded with water, blankets and donated amenity kits to Houston from Chicago's O'Hare International Airport on Tuesday. The first plane departed with 36,000 pounds of relief supplies, the airline told CNN.
American flew a 757 with supplies to Houston from Dallas late Monday, although it said the items on board were "for their team members." The plane departed Houston with employees of American and a regional airline it works with.
Several airlines evacuated customers who were stranded at the airports.
Southwest said it flew about 500 stranded passengers out of Houston's Hobby airport on Sunday.
Working without lights at the airport, airline crews raced against the setting sun, and the flights received special permission from the FAA, which had earlier in the day closed the airport.
On Monday, Spirit Airlines received special permission to evacuate 180 passengers from Bush airport. The airport said the passengers were taken to Chicago and Detroit.
It will be at least several days until the Houston airports reopen, and likely many days after that before air travel nation-wide returns to normal.
While far from the busiest air travel holiday in the US, an industry group had projected that 16.1 million people would travel in the week around Labor Day. Bush Airport is scheduled to re-open midday on Thursday and Hobby could re-open as early as Wednesday morning, according to the FAA.