Recovery teams have resumed the search for 12 members of two families who are missing after a rain-swollen river in Texas carried a holiday home off its foundation, slamming it into a bridge downstream.

The hunt for the missing picked up after a holiday weekend of terrible storms that dumped record rainfall on the American heartland, caused major flooding and spawned tornadoes and killed at least eight people in Oklahoma and Texas.

More than 1,000 homes have been damaged or destroyed in Texas, and thousands of residents are displaced.

Authorities were also searching for victims and assessing damage just across the Texas-Mexico border in Ciudad Acuna, where a tornado killed 13 people and left at least five unaccounted for.

Texas governor Greg Abbott declared disasters in 37 counties, allowing for further mobilisation of state resources to assist.

"You cannot candy coat it. It's absolutely massive," Mr Abbott said after touring the destruction.

The worst flooding damage was in Wimberley, where the holiday home was swept away, a popular tourist town along the Blanco River in the corridor between Austin and San Antonio.

Trey Hatt, a spokesman for the Hays County emergency operations centre, said that the "search component" of the mission was over, meaning no more survivors were expected to be found in the flood debris.

Witnesses reported seeing the swollen river push the home off its foundation and smash it into a bridge. Only pieces of the home have been found, Hays County Judge Bert Cobb said.

One person who was rescued from the home told workers that the other 12 inside were all connected to two families, Mr Cobb said. Young children were among those believed to be missing.

The Blanco River crested above 40ft - more than triple its flood stage of 13ft.

The river swamped a busy north-south highway and forced parts of it to close. 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 upstream.

Flooding wreaked havoc late on Monday afternoon in Austin, where emergency crews responded to more than 20 high-water rescues, and later in Houston, where the National Weather Service declared a flash flood emergency and an announcer at the Houston Rockets basketball game asked fans not to leave because of severe weather.

Harris County Flood District, which includes Houston, advised residents not to leave their homes after the weather service issued a flash flood warning for parts of the county. Before the sun rose, emergency crews used helicopters and boats to help residents evacuate their flooded homes.

The storm system also prompted reports of tornadoes across the state and was blamed for four deaths: 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 student who died on Saturday 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 across the state, which also saw severe flooding and reported tornadoes.

Houston police department spokesman Victor Senties confirmed two bodies were found in the city of Houston.

Harris County flood control district spokeswoman Kim Jackson said a third body was found in a vehicle on Interstate 45.

The National Weather Service said about 11 inches of rain fell in six hours in parts of south-west Houston.