US President Donald Trump has praised the rescue effort for tropical storm Harvey after arriving in the southern state of Texas, despite state authorities facing growing criticism over a decision to not evacuate Houston.

Speaking in Corpus Christi near where Harvey first came ashore last week, Trump on Tuesday said that he wanted the relief effort to stand as an example of how to respond to a storm.

"We want to be looked at in five years, in 10 years from now as, this is the way to do it," Trump told reporters during a meeting with officials from local, state and federal agencies.

READ MORE: Dams, levee overflow as Houston battles huge flooding

Since making landfall, the slow-moving storm has killed at least nine people, forced 30,000 people to seek emergency shelter and paralysed Houston, the fourth most-populous city in the country.

Harvey has continued to bring record-breaking rains and catastrophic flooding, drawing comparisons with Hurricane Katrina, which devastated New Orleans 12 years ago, killing 1,800 people.

Thousands seek shelter from floods after Harvey

Former President George W. Bush was widely criticised for his administration's handling of the response to that disaster, taking a heavy toll on public support of his administration.

Harvey, which has been downgraded from a hurricane to a tropical storm, is expected to reach Louisiana early on Wednesday - one day after the 12th anniversary of Katrina hitting the state.

Al Jazeera's Heidi Zhou-Castro, reporting from Houston, said that while many Trump supporters will be welcoming his visit, many others will be asking why more was not being done.

"Trump was congratulatory to federal agencies and how they've responded to this disaster but in the past four days, he hasn't acknowledged a major criticism - why people weren't told to evacuate before the flooding started.

"Trump is expected to visit the state capital of Austin to receive further briefings and speak to the press, where he will most likely face this and other critical questions about the management of the disaster."

Trump promises aid, questions raised

The president has promised federal assistance to storm-ravaged parts of Texas, insisting Congress will act swiftly on a multibillion-dollar recovery package.

"I think it'll happen very quickly," Trump said on Monday at a White House press conference. "It'll go very fast."

READ MORE: Hurricane Harvey - What you need to know

He said existing disaster balances of more than $3bn are sufficient for the immediate emergency but promised his administration will send lawmakers a request for far more to help Texas rebuild from the storm.

"The real number, which will be many billions of dollars, will go through Congress," Trump said.

More than 450,000 Harvey disaster victims expected to file for aid

Yet the president's pledge of swift action on billions of dollars in disaster aid is at odds with his proposed budget, which would eliminate the programme that helps Americans without flood insurance rebuild their homes and cut grants to states that would allow them to take long-term steps to reduce the risk of flooding before disaster strikes.

Trump's budget for 2018 zeroes out the Community Development Block Grants, a key scheme that helped the Gulf Coast rebuild after Hurricane Katrina and New York and New Jersey come back from Superstorm Sandy.

Among other things, the grants help people without flood insurance coverage rebuild their homes. In the 2017 budget, the Republican-led Congress restored some of the block grant money.

Thousands rescued

Some 3,500 people already have been rescued from high waters in the Houston area with police, firefighters and National Guard troops continuing to try to locate those marooned in high waters.

About 9,000 evacuees were staying at Houston's George R Brown Convention Center and Houston Mayor Sylvester Turner said his office had asked the Federal Emergency Management Agency for assets to allow the city to shelter another 10,000 people.

The storm broke Texas rainfall records at one measuring site south of Houston, which recorded 49.32 inches (1.25 metres) of precipitation since the storm's start. The rainfall is more than the region typically sees in a year and exceeds 48 inches (122cm) recorded in 1978.

Harvey has roiled energy markets and wrought damage estimated to be in the billions of dollars, with rebuilding likely to last beyond Trump's four-year term in office.

It is expected to produce another 6 to 12 inches (15-30cm) of rain through Thursday over parts of the upper Texas coast into southwestern Louisiana, the National Weather Service said.

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

Source: Al Jazeera and news agencies