HOUSTON — As more than a foot of rain deluged the nation’s fourth-largest city, inundating homes, shutting down major highways and leaving at least five people dead, Houston’s mayor said there was no immediate solution.

Heavy flooding has become nearly an annual rite of passage in the practically sea-level city, where experts have long warned of the potential for catastrophe.

“I regret anyone whose home is flooded again,” said Sylvester Turner, the city’s mayor, on Monday. “There’s nothing I can say that’s going to ease your frustration. We certainly can’t control the weather.”

“A lot of rain coming in a very short period of time, there’s nothing you can do,” he added.

Flash flooding and a 50 percent chance of more were possible Tuesday, a day after some areas saw water levels approaching 20 inches. The National Weather Service had the area under a flash flood watch through Wednesday morning.

Scores of subdivisions were flooded and most schools remained closed although the city itself was returning to normal. Municipal offices reopened Tuesday and by midmorning, less than 10,000 CenterPoint Energy customers were without power, an improvement from 24 hours earlier when electricity outages topped 100,000. Houston’s Metropolitan Transit Authority resumed service and most highways within the city were open.