Floodwaters from Tropical Storm Harvey, which has already killed at least seven people in Texas and is expected to drive tens of thousands from their homes, will likely rise in the coming days as heavy rains 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 of people 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 came ashore on Friday near Corpus Christi, 350km south of Houston.

The worst is far from over, as the National Weather Service issued numerous flood warnings across the region.

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 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, 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 neighbouring Montgomery County when a tree fell on her trailer home while she slept, the local medical examiner said on Twitter.

With other people missing, the death toll could rise.

Both of Houston’s major airports were shut down, along with most major highways, rail lines and a hospital, where patients were evacuated over the weekend.

As of Monday evening 267,000 Texans were left without power in the southeast corner of the state.

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 recognise 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 25-50cm 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 rescued at least 2000 people so far, plucking many from rooftops by helicopter.

They have urged the hundreds more believed to be marooned in flooded houses to hang towels or sheets outside to alert rescuers.

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

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

About 5500 people were in shelters as of Monday morning, with Federal Emergency Management Agency director Brock Long forecasting that 30,000 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. .

“I’m not complaining, we’re alive,” said Costilla.

“When I saw the forecast of the storm I said I’ll be happy if we get out with our lives.”

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

Gasoline futures hit their highest in two years as Harvey shut down multiple refiners, knocking out about 13 per cent of total US refining capacity.

The floods’ path of destruction could destroy as much as $20 billion in insured property, making it one of the costliest storms in history for US insurers, according to Wall Street analysts.

By Marianna Parraga and Ernest Scheyder