Torrential rains in Texas, which caused flooding that killed 16 people this week, have spread to southern Louisiana, leaving parts of that state and Mississippi under a flash flood watch through Sunday morning, according to the National Weather Service.

Heavy rains could strike the Florida panhandle early next week, but not as intensely as in Texas, Daniel Petersen, a meteorologist at the Weather Prediction Centre in Maryland, said in a phone interview on Saturday.

Small streams in southern Louisiana have overflowed their banks, causing localised flooding, he added.

At least 16 people have died in Texas in the past week as some rivers swelled to levels not seen in more than 100 years, forcing thousands of people to evacuate their homes in low-lying areas.

Texas Governor Greg Abbott has declared a state of disaster in more than 30 counties, the Texas Department of Public Safety said in a statement on Saturday. In Bastrop County, southwest of the state capital of Austin, flooding damaged nearly 300 homes, it added.

Heavy rainfall was forecast to continue on Saturday along the Texas coast and potentially trigger more flooding there, state and federal officials said.

National Weather Service hydrologist Gregory Waller said in a phone interview on Saturday that the Brazos River was expected to crest this weekend near Rosharon, a community south of Houston that is home to more than 1,500 people.

The Texas Department of Criminal Justice began evacuating on Friday about 1,700 inmates at its Ramsey Unit in Rosharon, due to flooding along the Brazos.

Flooding struck Richmond, upriver from Rosharon, earlier this week when the Brazos overflowed its banks and according to state officials damaged nearly 80 homes.

Forecasters said the threat of flash floods in Texas on Sunday would decrease as rains become less intense.

"We think that tomorrow, the lower rain totals are going to give them a chance to dry out," Petersen said.

Even after the rains stop, parts of the state are likely to have a challenging path to recovery.

Abbott on Friday toured flooded areas south of Houston and told reporters some neighbourhoods were "literally islands, completely surrounded by water."

Nine soldiers died on Thursday when their troop carrier overturned during a training exercise at the U.S. Army base of Food Hood in the central part of the state, in a region where torrential rains caused flash flooding.