IN PICTURES | Hurricane Harvey: A black cloud over Texas

Tropical Storm Harvey dumped more rain on Houston on Monday, worsening flooding that has paralysed the US's fourth-biggest city, forced thousands to flee surrounding counties and swollen rivers to levels not seen in centuries.

Harvey, the most powerful hurricane to hit Texas in more than 50 years, first landed late on Friday and has killed at least two people. It has since stayed around the Gulf of Mexico coast where it is forecast to remain for several more days, drenching parts with a year's worth of rain in the span of a week.

Schools, airports and office buildings in Houston, home to about 2.3 million people, were ordered shut on Monday as scores of roads turned into rivers and chest-high water filled suburbs in the low-lying city.

Torrential rain also hit areas more than 240km away, swelling rivers upstream and causing a surge that was heading towards the Houston area.

Authorities ordered more than 50,000 people to leave parts of Fort Bend County, about 55km southwest of Houston, as the Brazos River was set to crest at a record high of 18m this week, 4.3m above its flood stage - a high not seen in at least 800 years.

"What we're seeing is the most devastating flood event in Houston's recorded history," said Steve Bowen, chief meteorologist at reinsurance firm Aon Benfield.

Total precipitation could reach 12cm in some coastal areas of Texas by the end of the week, or the average rainfall for an entire year, forecasters said. Nearly 61cm fell in a span of 24 hours in Baytown, a city home to major refineries about 48km east of Houston, the National Weather Service said.

"Water started flooding our house and by last night we were unable to leave," said Maria Davila, one of about 1000 people in a makeshift "mega shelter" at Houston's convention centre, which is set up to house 5,000 evacuees.

US President Donald Trump plans to go to Texas on Tuesday to survey damage. Facing the first big US natural disaster since he took office in January, he signed a disaster proclamation on Friday, triggering federal relief efforts. Texas Governor Greg Abbott said on Sunday he plans to add 1,000 more National Guard personnel to the flood battle.

Harvey is expected to produce an additional 38cm to 64cm of rain this week in the upper Texas coast and into southwestern Louisiana, the National Hurricane Centre said.

The centre of Harvey was 154km southwest of Houston on Monday morning and is forecast to arc slowly towards the city on Wednesday.

"The storm isn't moving much. If it doesn't move much, it keeps throwing rain into the same area," said Steve Wistar, a meteorologist with AcuWeather.

The Harris County Sheriff's Office used motorboats, airboats and other vehicles to rescue more than 2,000 people in the Houston area on Sunday.

The US Coast Guard and Houston police rescued hundreds more as residents brought boats to staging centres to help and helicopters were deployed to save others stranded by the floods.

The National Weather Service has issued flood watches and warnings from San Antonio to New Orleans, an area home to more than 13 million people.

Federal authorities predicted it would take years to repair the damage caused by Harvey. In comparison, Hurricane Katrina devastated New Orleans and killed 1,800 people in 2005. It resulted in more than $15-billion in flood insurance losses. Flood damage in Texas from Hurricane Harvey may equal that from Katrina, the costliest natural disaster in US history. The Gulf is home to almost half of the nation's refining capacity, and the reduced supply could affect petrol supplies across the US. Shutdowns included Exxon Mobil's Baytown refinery, the second-largest US refinery.

The outages will limit the availability of US crude, petrol and other refined products for global consumers and further push up prices, analysts said. All Houston port facilities were closed on Monday because of the weather threat.

More than 229,000 customers in the Houston area were without power on Monday morning. Houston's George Bush Intercontinental Airport, one of the nation's busiest, halted all commercial flights on Sunday.

Jose Rengel, who lives in Galveston, said he saw water cresting the tops of cars. "I am blessed that not much has happened to me, but these people lost everything. And it keeps raining," he said. "The water has nowhere to go." - Reuters