Torrential rain left much of Texas swamped on 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.

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

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.