US disaster agency says 50 counties in Texas are affected by the flooding, as weather forecasters predict more rain.
Floodwaters reached the rooflines of single-story homes on Monday and people could be heard pleading for help from inside as Harvey poured rain on the Houston area for a fourth consecutive day after a chaotic weekend of rising water and rescues.
The nation’s fourth-largest city remained mostly paralyzed by one of the largest downpours in US history. And there was no relief in sight from the storm that spun into Texas as a Category 4 hurricane, then parked over the Gulf Coast.
Rescuers continued plucking people from the floodwaters. Mayor Sylvester Turner put the number rescued by police at more than 3,000.
The coastguard said it also had rescued more than 3,000 by boat and air and was taking more than 1,000 calls her hour.