Houston Mayor Sylvester Turner said the city expected most public services and businesses to be restored by Tuesday, the first day after Monday's Labor Day holiday.
"Over 95 percent of the city is now dry. And I'm encouraging people to get up and let's get going," Turner told NBC News.
Even so, Houston mandated the evacuation of thousands of people on the western side of town on Sunday to accommodate the release of water from two reservoirs that otherwise might sustain damage. The storm stalled over Houston, dumping more than 50 inches (1.3 m) on the region.
Houston cut off power to homes on Sunday to encourage evacuations. The area was closed off on Sunday and military vehicles were stationed on the periphery to take people out.
Karen Waltmon, 58, who was returning to her home in one of the neighborhoods, said she wondered if parts of the city would have to be razed.
"I feel a lot of Houston is drying out, and I don't want them to forget about us," she said.
About 37,000 refugees stayed overnight in 270 shelters in Texas plus another 2,000 in seven Louisiana shelters, the highest number reported by the American Red Cross.
Some 84,700 homes and businesses were without power on Sunday, down from a peak of around 300,000, according to the region's major electric companies.
In Crosby, Texas, an Arkema chemical plant that ran out of electricity needed to keep volatile organic peroxide refrigerated will burn the remaining containers as a "proactive measure," company and Harris County fire officials said in a statement.
Officials last week evacuated residents and set up a 1.5-mile (2.4-km) perimeter around the area.
Energy disruptions pushed up gasoline futures to a two-year high ahead of the holiday weekend, but major refineries started to come back online on Friday.
Colonial Pipeline, the biggest U.S. fuel system, expects to reopen a Texas segment of its network on Monday, when it will resume transporting distillates from Houston to Hebert, Texas,
the company said on Sunday, adding that it would be ready to start moving gasoline on Tuesday.
Those repairs would restore to normal Colonial's entire pipeline from Houston to Linden, New Jersey, relieving shortages between Texas and the U.S. Northeast.