HOUSTON -- Floodwaters deepened across much of Texas on Tuesday as storms dumped almost another foot of rain on the Houston area, stranding hundreds of motorists and inundating the famously congested highways that serve the fourth-largest U.S. city.

Meanwhile, the search went on for at least 13 people who were still missing, including a group that disappeared after a vacation home was swept down a river and slammed into a bridge.

Several more fatalities were reported -- four in Houston and one more in Central Texas. That brought to 14 the number of people killed by the holiday weekend storms in Texas and Oklahoma.

Similar search efforts unfolded just south of the Texas-Mexico border, where crews tried to track down the missing and assessed damage in the city of Ciudad Acuna after a tornado killed 13 people Monday.

In Houston, the water rose sharply overnight as about 11 more inches of rain fell, much of it in a six-hour period. By Tuesday evening, most rivers had receded back within their banks.

The floodwaters affected virtually every part of the city and paralyzed some areas. Firefighters carried out more than 500 water rescues, most involving stranded motorists. At least 2,500 vehicles were abandoned by drivers seeking higher ground, officials said.

"Given the magnitude and how quickly it happened, in such a short period of time, I've never seen this before," said Rick Flanagan, Houston's emergency management coordinator.

The drenching weather threatened to linger. Forecasts called for a 20 to 40 per cent chance of thunderstorms through the rest of the week in Houston.

The flooding closed several highways, and the ones that stayed open became a gridlocked mess.

Flooding in Houston, Texas
Roberto Salas, left, and Lewis Sternhagen check a flooded car in Houston, Tuesday, May 26, 2015. (Marie D. De Jesus / Houston Chronicle)

Interstate 45 near downtown was backed up for miles on Tuesday morning, and a handful of motorists traveled the wrong way on the highway to retreat from high water.

The small cars weaved between massive 18-wheelers as other drivers stared at them in disbelief. With no end to the backup in sight, some drivers got off the freeway, only to be held up again by water covering nearby access roads.

In the Heights neighbourhood about 8 kilometres from downtown, groups of people roamed the streets after escaping their stalled cars, and police cruisers blocked some dangerous roads.

Some motorists were stuck on I-45 all night, sleeping in their cars until the backup was cleared about 8 a.m.

NBA fans at the Toyota Center, where the Rockets hosted a Western Conference finals game against Golden State on Monday, were asked with about two minutes left in the game not to leave the arena because of the weather.

The game ended before 11 p.m., but about 400 people remained in their seats at 1:30 a.m., choosing to stay in the building rather than brave the flooded roads that awaited them outside. Up to 150 people stayed all right, according to arena officials.

A spokeswoman for the flood district of Harris County, which includes Houston, said up to 700 homes sustained some level of damage.

Family home swept away in Texas flooding
Hudson Doty, 18, left, and Grant Guzal, 17, right, walk near the foundation of a family in Wimberley, Texas, on Monday, May 25, 2015. (Rodolfo Gonzalez / Austin American-Statesman)

Yesenia Lopez and husband, Armando, waded through knee-deep water, carrying bags of possessions over their heads. During the night, a nearby bayou overflowed and flooded their apartment complex.

"We tried to do as much as we could, saved the family portraits and stuff like that, but everything else is destroyed," she said.

The two planned to stay with her mother-in-law.

Dripping with water, she said: "Everything is scary. That's the first time I lived through something like this, so it gives you a lot to think about."

Officials in Hays County, about 290 kilometres west of Houston, said 30 people who had been reported as missing were accounted for by mid-afternoon Tuesday.

Some of the worst flooding in Texas was in Wimberley, a popular tourist town along the Blanco in the corridor between Austin and San Antonio. That's where the vacation home was swept away.

Flooding in Austin
Rescuers grab the hand of a man stranded in rushing water in Austin, Texas on May 25, 2015. (Alberto Martinez / Austin American Statesman)

The "search component" of the mission ended Monday night, meaning no more survivors were expected to be found, said Trey Hatt, a spokesman for the Hays County Emergency Operations Center.

Eight of those missing from the destroyed house were friends and family who had gathered for the holiday, said Kristi Wyatt, a spokeswoman for the City of San Marcos. She said three more were members of another family in a separate situation. An unrelated person was also missing, Wyatt said.

Members of the National Guard in Texas search
Members of the National Guard work along the Blanco River with a search and rescue team, in Wimberley, Texas, Tuesday, May 26, 2015. (AP / Eric Gay)

Young children were believed to be among the missing.

The Blanco crested above 40 feet -- more than triple its flood stage of 13 feet. The river swamped Interstate 35 and closed parts of the busy north-south highway. Rescuers used pontoon boats and a helicopter to pull people out.

Hundreds of trees along the Blanco were uprooted or snapped, and they collected in piles of debris up to 20 feet high.

The deaths in Texas included a man whose body was pulled from the Blanco; a 14-year-old who was found with his dog in a storm drain; a high school senior who died after her car was caught in high water; and a man whose mobile home was destroyed by a reported tornado.

The Oklahoma Department of Emergency Management also reported four fatalities between Saturday and Monday after severe flooding and reports of tornadoes.

People help in clearing debris from Mexico tornado
People help clear debris after a powerful tornado swept through Ciudad Acuna Monday, May 25, 2015. (AP)

In Ciudad Acuna, Mayor Evaristo Perez Rivera said 300 people were treated at local hospitals after the twister, and more than 200 homes had been completely destroyed in the city of 125,000 across from Del Rio, Texas.

Thirteen people were confirmed dead -- 10 adults and three infants, including one that was ripped from its mother's arms by the storm.