The storm caused by Hurricane Harvey is now spinning across Texas into Louisiana, sending more people fleeing for shelter after flooding in Houston killed at least 25 and drove tens of thousands from their homes.

The slow-moving storm has forced 32,000 people to seek shelter since coming ashore on Friday near Corpus Christi, Texas, as the most powerful hurricane to hit Texas in more than half a century.

On Wednesday, it pummelled parts of the coast from Port Arthur, Texas, to Lake Charles, Louisiana.

Among the latest deaths reported were two people who drowned while driving through high water near Simonton, Texas, 64 kilometres west of Houston, Major Chad Norvell of the Fort Bend County Sheriff’s Office said on Twitter.

Houston’s KHOU-TV is also reporting that an infant girl was swept away by floodwaters as her parents were driving from Houston toward Louisiana on Highway 150.

Police in Harris County, home to Houston, said 17 people remained missing.

Busloads of people fleeing floodwaters around Port Arthur arrived in Lake Charles, joining local residents who had already packed into shelters to escape waterlogged homes.

Hurricane Harvey is forecast to drop a further 7.5-15 centimetres of rain on Wednesday, with a storm surge of up to 1.2 metres along the western part of Louisiana’s Gulf Coast.

The floods shut the nation’s largest oil refinery in Port Arthur in the latest hit to US energy infrastructure that has sent gasoline prices climbing and disrupted global fuel supplies.

Moody’s Analytics is estimating the economic cost from Harvey for southeast Texas at $US51 billion ($A65 billion) to $US75 billion, ranking it among the costliest storms in US history.

“The worst is not yet over for southeast Texas as far as the rain is concerned,” Governor Greg Abbott said.

He warned residents of storm-hit areas to expect floodwaters to linger for up to a week and said the area affected was larger than that hit by 2005’s Hurricane Katrina, which killed more than 1,800 people in New Orleans, and 2012’s Superstorm Sandy, which killed 132 around New York and New Jersey.

The population of Houston’s metropolitan area is about 6.5 million, far greater than New Orleans’ at the time of Katrina.

Governor Abbott asked that the federal government spend more on rebuilding Texas’ Gulf Coast than it did after the earlier storms.

US President Donald Trump opened a speech on tax reform in Springfield, Missouri, on Wednesday with a pledge to stand by the people of Texas and Louisiana.

He visited Texas on Tuesday to survey damage from the first major natural disaster of his presidency.

“We are here with you today … and we will be with you every single day after to restore, recover and rebuild,” he said on Wednesday.

Goldman Sachs economists say the storm has reduced the chance of President Trump acting on his threat to shut the federal government over funding for a border wall with Mexico from 50 per cent to 35 per cent.

Clear skies in Houston on Wednesday brought relief to the energy hub and fourth-largest US city after five days of catastrophic downpours with Houston airports beginning limited services.

Hurricane Harvey made landfall for a third time early on Wednesday, and was about 80km north of Lake Charles, near the Texas border at 4pm (local time), the US National Hurricane Center said.