With its flood defences strained, the crippled city of Houston anxiously watched dams and levees Tuesday to see if they would hold until the rain stops, and meteorologists offered the first reason for hope — a forecast with less than a centimetre of rain and even a chance for sunshine.

The human toll continued to mount, both in deaths and in the ever-swelling number of scared people made homeless by the catastrophic storm that is now the heaviest tropical downpour in U.S. history.

The city's largest shelter was overflowing when the mayor announced plans to create space for thousands of extra people by opening two and possibly three more mega-shelters.

"We are not turning anyone away. But it does mean we need to expand our capabilities and our capacity," Mayor Sylvester Turner said. "Relief is coming."

The rescues went on. Federal and local agencies said they had lifted more than 13,000 people out of the floodwaters in the Houston area and surrounding cities and counties.

Louisiana's governor offered to take in Harvey victims from Texas, and televangelist Joel Osteen opened his Houston megachurch, a 16,000-seat former arena, after critics blasted him on social media for not acting to help families displaced by the storm.

'The end of the beginning'

Meteorologists said the sprawling city would soon get a chance to dry out.

When Harvey returns to land Wednesday, "it's the end of the beginning," National Hurricane Center meteorologist Dennis Feltgen said.

Harvey will spend much of Wednesday dropping rain on Louisiana before moving on to Arkansas, Tennessee and parts of Missouri, which could also see flooding.

But Feltgen cautioned: "We're not done with this. There's still an awful lot of real estate and a lot of people who are going to feel the impacts of the storm."

Drone video over Houston shows extent of flooding1:31

The National Weather Service predicted less than a centimetre of rain for Houston on Wednesday and only a 30 per cent chance of showers and thunderstorms for Thursday. Friday's forecast called for mostly sunny skies with a high near 34 C.

Early Wednesday morning, Harvey had made another landfall just west of Cameron, La., with sustained winds of 72 km/h, the National Hurricane Center reported. 

In all, more than 17,000 people have sought refuge in Texas shelters, and that number seemed certain to increase, the American Red Cross said.

The city's largest shelter, the George R. Brown Convention Center, held more than 9,000 people, almost twice the number officials originally planned to house there. The crowds included many from outside Houston.

By the end of the day, the Toyota Center, home of the NBA's Rockets, had begun accepting people who could not find space at the convention centre.

APTOPIX Harvey

Demetres Fair holds a towel over his two-year-old daughter, Damouri, as they are rescued by boat during flooding in Houston on Monday. (Gerald Herbert/Associated Press)

Louisiana Gov. John Bel Edwards said he expected Texas officials to decide within 48 hours whether to accept his offer to shelter storm victims, which comes as Louisiana deals with its own flooding. About 500 people were evacuated from flooded neighbourhoods in southwest Louisiana, Edwards said.

The city has asked the Federal Emergency Management Agency for more supplies, including cots and food, for an additional 10,000 people, said the mayor, who hoped to get the supplies no later than Wednesday.

In an apparent response to scattered reports of looting, the mayor also imposed a curfew. Police Chief Art Acevedo said violators would be questioned, searched and arrested.

At least 18 deaths so far

Four days after the storm ravaged the Texas coastline as a hurricane, authorities and family members have reported at least 18 deaths from Harvey. They include a woman killed when heavy rain sent a large oak tree crashing onto her trailer and another woman who apparently drowned after her vehicle was swept off a bridge.

The Harris County Institute of Forensic Sciences updated its storm-related deaths Tuesday night to include an 89-year-old woman, Agnes Stanley, who was found floating in 1.2 metres of floodwater in a home. A 76-year-old woman was found floating in floodwater near a vehicle. Her name was not released. A 45-year-old man, Travis Lynn Callihan, left his vehicle and fell into floodwaters. He was taken to a hospital, where he died Monday.

Houston police confirmed that a 60-year-old officer drowned in his patrol car after he became trapped in high water while driving to work. Sgt. Steve Perez had been with the force for 34 years.

Six members of a family were feared dead after their van sank into Greens Bayou in East Houston. A Houston hotel said one of its employees disappeared while helping about 100 guests and workers evacuate the building.

Authorities acknowledge that fatalities from Harvey could soar once the floodwaters start to recede.

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People sleep on the floor at the George R. Brown Convention Center that has been set up as a shelter for evacuees escaping the floodwaters in Houston. (LM Otero/Associated Press)

A pair of 70-year-old reservoir dams that protect downtown Houston and a levee in a suburban subdivision began overflowing Tuesday, adding to the rising floodwaters.

Engineers began releasing water from the Addicks and Barker reservoirs Monday to ease the strain on the dams. But the releases were not enough to relieve the pressure after the relentless downpours, Army Corps of Engineers officials said. Both reservoirs are at record highs.

The release of the water means that more homes and streets will flood, and some homes will be inundated for up to a month, said Jeff Linder of the Harris County Flood Control District.

The levee was later fortified, but officials said they did not know how long the work would hold.

Infrastructure at risk

Officials in Houston were also keeping an eye on infrastructure such as bridges, roads and pipelines that are in the path of the floodwaters.

Water in the Houston Ship Channel, one of the nation's busiest waterways, which serves the Port of Houston and Houston's petrochemical complex, is at levels never seen before, Linder said.

The San Jacinto River, which empties into the channel, has pipelines and roads and bridges not designed for the current deluge, Linder said, and the chance of infrastructure failures will increase the "longer we keep the water in place."

Among the worries: debris coming down the river and crashing into structures and the possibility that pipelines in the riverbed will be scoured by swift currents. In 1994, a pipeline ruptured on the river near Interstate 10 and caught fire.

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U.S. President Donald Trump and his wife Melania Trump depart the White House Tuesday on their way to view storm damage in Texas. (Kevin Lamarqu/Reuters)

During a visit to the storm zone, President Donald Trump kept his distance from the epicentre of the damage in Houston to avoid disrupting recovery operations. But he planned to return to the region Saturday to meet with some of the victims, press secretary Sarah Huckabee Sanders said.

Record rainfall

After five consecutive days of rain, Harvey set a new continental U.S. record for rainfall for a tropical system.

The rains in Cedar Bayou, near Mont Belvieu, Texas, totalled 132 centimetres as of Tuesday afternoon. That's a record for both Texas and the continental United States, but it does not quite surpass the 133 centimetres from Tropical Cyclone Hiki in Kauai, Hawaii, in 1950, before Hawaii became a state.

The previous record was 122 centimetres set in 1978 in Medina, Texas, by Tropical Storm Amelia. A weather station southeast of Houston reported 125 centimetres of rain.

Before it breaks up, Harvey could creep as far east as Mississippi by Thursday, meaning New Orleans, where Hurricane Katrina unleashed its full wrath in 2005, is in Harvey's path. Foreboding images of Harvey lit up weather radar screens on the 12th anniversary of the day Katrina made landfall in Plaquemines Parish.

The disaster is unfolding on an epic scale, with the nation's fourth-largest city mostly paralyzed by the storm that arrived as a Category 4 hurricane and then parked over the Gulf Coast. The Houston metro area covers about 25,900 square kilometres, an area slightly bigger than New Jersey.

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A home in Spring, Texas, is surrounded by floodwaters on Monday. (David J. Phillip/Associated Press)