At least four people have died after Hurricane Beryl ripped through Texas late on Monday.
Russell Richardson, a 54-year-old information security officer called in to help with relief efforts, died when his vehicle flooded while he was driving to work, police in Houston said.
At least two people were killed when trees fell on homes, one of them a woman in Benton, Louisiana, according to Bossier Sheriff Julian Whittington.
Some local media reports suggest up to six people have been killed by fallen trees or by drowning.
More than 2.4 million homes and businesses in the state were left without power after the storm – re-classified to a tropical storm on Monday – knocked out 10 long-distance transmission lines and toppled hundreds of trees, some of which took down local power lines.
Almost two million of those affected are customers of CenterPoint Energy, Houston’s main electricity provider, which has said it hopes to restore services to half of them by Thursday, according to NBC, Sky’s US partner, quoting PowerOutage.us.
Texas lieutenant governor Dan Patrick said the company was bringing in thousands of additional workers to restore power, and prioritising places such as nursing homes and assisted living centres.
Mr Patrick said: “We’re not past any difficult conditions,” and predicted a “multiple day process to get power restored”.
Dozens of vehicles were left stranded on flooded roads as heavy rains swamped parts of the state.
Houston, the fourth-largest city in the US, suffered much of the damage as Beryl’s rains pounded coastal areas, but there were no immediate reports of structural damage.
Video of the dramatic rescue of man who had climbed to the roof of his pickup truck after it got trapped in fast-flowing waters was broadcast by local TV stations.
Emergency crews used an extension ladder from a fire truck to drop him a life jacket and a rope before moving him to dry land, one of at least 25 water rescues in the city, mostly for people with vehicles stuck in floodwaters.
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In May, eight people died and nearly one million were left without power as a previous set of storms hit the city.
Houston mayor John Whitmire said: “First responders are putting their lives at risk. That’s what they’re trained for. It’s working.”
Damaging winds and flash flooding would continue as Beryl pushes inland, forecasters said.
With parts of the area sweltering in a heatwave, restoring power is an urgent requirement, even though temperatures cooled slightly with the storm.
Beryl weakened further into a tropical depression, the National Hurricane Centre said on Monday evening, before moving eastwards, putting several other states at risk.
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It is forecast to weaken further to become a post-tropical cyclone on Tuesday.
As it moved inland, the storm threatened to create tornadoes and the US National Weather Service confirmed on social media that tornadoes had been spotted in northeastern Louisiana.