He said rain continues to fall and flooding in certain areas may last another week.
More than 20 people are reported dead, and large parts of the city of Houston are under water.
The storm has now moved on to neighbouring Louisiana, where flash-flood warnings have been issued.
Governor Abbott said Texas has carried out more than 8,500 rescues, and more than 32,000 people remain in shelters throughout the state.
Another 10,000 members of the National Guard are said to be on their way, joining the 14,000 already deployed to tackle the disaster.