Floodwaters from Tropical Storm Harvey, which has already killed at least seven people in Texas and was expected to drive tens of thousands from their homes, are likely to rise, officials warned on Monday, as heavy rain continued to pound the US Gulf Coast.

National Guard troops, police officers, rescue workers and civilians raced in helicopters, boats and special high-water trucks to rescue the hundreds still stranded in and around Houston, the nation's fourth-largest city.

The storm was the most powerful hurricane to strike Texas in more than 50 years when it hit land on Friday near Corpus Christi, 220 miles (354 km) south of Houston, and the worst is far from over, as the National Weather Service issued numerous regional flood warnings.

US President Donald Trump plans to go to Texas on Tuesday to survey the damage and may, in the future, visit Louisiana, where the storm is now dumping rain.

Trump, facing the biggest US natural disaster since he took office in January, has signed disaster proclamations for Texas and Louisiana, triggering federal relief efforts.

Harvey has killed at least six people in Harris County, where Houston is located, said Tricia Bentley, a spokeswoman for the county coroner's office, including a man who died in a house fire on Friday night and an elderly woman driving through flooded streets on the city's west side the next day.

A 60-year-old woman died in neighboring Montgomery County when a tree fell on her trailer home while she slept, the medical examiner said on Twitter. With others missing, the toll could rise.

Both of Houston's major airports were shut, along with most major highways, rail lines and a hospital, where patients were evacuated over the weekend. By Monday evening, 267,000 Texans had been left without power in the state's southeast corner.

One of three main rivers crossing Houston, the Brazos, was expected to crest sometime on Tuesday at 59 feet (18 meters), the National Weather Service said. The San Jacinto River was expected to crest over Interstate 10, the city's major east-west artery.

Rising river and reservoir levels forced the order of additional evacuations in the counties of Brazoria, Galveston and Fort Bend.

As stunned families surveyed the wreckage of destroyed homes and roads flooded or clogged with debris, Texas Governor Greg Abbott warned Houstonians to brace for a long recovery.

"We need to recognize this is going to be a new and different normal for this entire region," Abbott said.

Harvey was expected to linger over Texas' Gulf Coast for the next few days, dropping another 10 to 20 inches (25 to 51 cm) of rain, with threats of flooding extending into Louisiana.

In scenes evoking the aftermath of Hurricane Katrina in 2005, police and Coast Guard teams have each rescued more than 3,000 people, plucking many from rooftops by helicopter, as they urged the hundreds more believed to be marooned in flooded houses to hang towels or sheets outside to alert rescuers.

Harvey's center was about 100 miles (160 km) south of Houston and forecast to arc slowly toward the city through Wednesday, when the worst floods are expected, as well as on Thursday.

Schools and office buildings were closed throughout the metropolitan area, home to 6.8 million people, as chest-high water filled some neighborhoods in the low-lying city.

The US Army Corps of Engineers said on Monday it was releasing water from the nearby Addicks and Barker reservoirs into Buffalo Bayou, Houston's primary body of water.

"The more they release it could go up and it could create even additional problems," Houston Mayor Sylvester Turner warned. But the release was said to be necessary to prevent an uncontrolled surge of water, which Turner said "would be exponentially worse."

Torrential rain also hit areas more than 150 miles (240 km) away, swelling rivers and causing a surge that was heading toward Houston, where numerous rivers and streams already have been breached.

The Federal Emergency Management Agency director Brock Long estimated that 30,000 people would eventually be housed temporarily in shelters.

Regina Costilla, 48, said she and her 16-year-old son had been rescued from their home by a good Samaritan with a boat. She worried until she was reunited with her husband and dog, who had been left behind because they did not fit into the boat.

"I'm not complaining; we're alive," she said.

In Rockport, National Guard troops distributed water to residents as utility crews worked to restore power, amid reports of sporadic looting.

Resident Savannah White, 20, welcomed the president's visit because the city needs help.

"I'm glad to see him coming down here because it's in such bad condition," White said. "Pretty much destroyed, there's nothing left standing."

Houston did not order an evacuation due to concerns about people being stranded on city highways now consumed by floods, Turner said.

Abbott, who had suggested on Friday that people leave the area, declined to second-guess the mayor on Monday, telling reporters, "Decisions about evacuations are something that are behind us."

Gasoline futures hit their highest in two years as Harvey knocked out about 13 percent of total U.S. refining capacity, based on company reports and Reuters estimates.

The United States' second-largest refinery, in Baytown, was shut down, and the largest refinery, in Port Arthur, was expected to make a final decision on shutdown on Tuesday.

The floods could destroy as much as $20 billion in insured property, making the storm one of the costliest in history for US insurers, Wall Street analysts say.