Big airports in Florida remained closed Monday, and flight cancellations were spreading north along the track of Tropical Storm Irma.
American Airlines said it won't resume flights in Miami until at least Tuesday, revising its plans to restart late Monday.
An airline spokesman said the timetable depended on approval by federal aviation officials and the ability of security screeners and airport vendors to return to work.
Terminal buildings at the Miami airport suffered significant damage, and ceiling tiles at gate areas fell down throughout the airport, said spokesman Greg Chin. He said around midday that crews were drying areas.
At nearby Fort Lauderdale-Hollywood International Airport, there were some leaks in terminal roofs and trees were downed in the employee parking lot, but overall damage was minimal, said spokesman Greg Meyer. He said water on the runways was receding.
Airlines were expected to fly empty planes to the Fort Lauderdale airport later Monday to operate departing flights Tuesday morning, Meyer said.
More than 3,900 U.S. flights scheduled for Monday were canceled by late morning - and more than 9,000 since Saturday - according to tracking service FlightAware.
Disruptions have spread beyond Florida. Delta Air Lines canceled 900 flights Monday, including many at its Atlanta hub because of high winds. American canceled 300 flights in Charlotte, North Carolina, due to wind.
Still, Irma weakened from a hurricane to a tropical storm and didn't cause as much damage in Florida as some forecasters had feared. Stocks rose, including airlines.
Shares of American Airlines Group Inc., Delta Air Lines Inc., United Continental Holdings Inc., JetBlue Airways Corp., and Spirit Airlines Inc. all gained at least 2 percent in midday trading. Spirit, JetBlue and American were the biggest risers in percentage terms - those three have a greater percentage of flights in Florida and the Caribbean than do their rivals, according to a Raymond James analyst.