Torrential rain left much of Texas swamped Wednesday after wild weather killed at least 28 people in the United States and Mexico, and Houston's mayor warned more flooding could be in store.

The southern US states of Texas and Oklahoma, and northern Mexico, have borne the brunt of several days of violent weather, including tornadoes, which have left scores dead, missing or injured on both sides of the border.

Rain was falling at over an inch an hour early Wednesday in the Dallas area, prompting flash flood warnings from national forecasters.

More than 10 inches (25 centimetres) of rain fell in just a few hours in the Texas city of Houston Tuesday, triggering the worst flooding there in at least a decade.

Hundreds of vehicles, some fully under water, were abandoned on Houston's roads.

People were trapped in their cars, while others were marooned in their homes, as flood waters rose menacingly around them.

Two people died overnight due to the flooding in the city, Mayor Annise Parker said.

"I want to ask and urge people to continue to be safe and recognize that we may have more rain later today," she said, encouraging residents of America's fourth-largest city to stay at home.

"We have cars littered all over the city," she told a press conference, adding that emergency crews were attempting to reach the abandoned vehicles to see if anyone had been trapped inside.

Parker cautioned that more life-threatening conditions could face locals again this week.

Some 100,000 gallons of wastewater spilt in the Houston area after the massive rainfall damaged a water treatment plant, the Houston Chronicle reported.

President Barack Obama called the flooding in Texas "terrible" and said he had offered urgent assistance to state Governor Greg Abbott.

- 'I love you. And pray' -

Texas authorities said 13 people have been killed across the sprawling state in the weekend storms, at least four of them in Houston. Fears were growing meanwhile for at least 11 people still missing in Hays County, also in Texas.

Two more died in Oklahoma, north of Texas.

Many of the dozen missing in Hays County were from one house that was torn from its foundations during a terrifying flash flood over the weekend.

There were two families staying at the A-frame house in the picturesque town of Wimberley for the long Memorial Day weekend, NBC News reported. Among them were three children.

Inside was Laura McComb, who was on the phone with her sister when the house, built on stilts, broke free and was swept away.

"We are in a house that is now floating down the river," she reportedly told her sister, Julie Shields. "Call Mom and Dad. I love you. And pray."

Shields told the NBC affiliate KXAN that the phone call ended when McComb thought she saw a light from a helicopter that had come to rescue them.

She has not been heard from since Saturday night.

- Baby found dead -

South of the border, Mexico has also felt nature's wrath.

A savage tornado roared through the border town of Ciudad Acuna at dawn Monday, killing at least 13 people and flattening hundreds of homes in a deadly six-second blast.

Among the victims of its 270-300 kilometre-per-hour (168-186 mile) winds was a baby boy who was ripped from the grasp of his desperate parents and flung into the air.

His body was found on Tuesday after a frantic search.

The child was "catapulted by the tornado," Mayor Evaristo Lenin Perez said.

"It was horrible. It started raining in the morning. Very early, the wind came and everything started to fly around and then it all fell to the ground," Ciudad Acuna resident Juanita Perez said tearfully.

The federal government said the tornado destroyed 247 homes and damaged another 450.

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