He told Metro US: 'Harvey is expected to produce additional rainfall accumulations of 15 to 25 inches through Friday over the upper Texas coast and into southwestern Louisiana. There's the possibility of another 50 inches of rain pounding the next path in its destruction before it finally dissipates.
Thousands of people have already been rescued from "catastrophic" flooding in affected areas of the state, while further thousands of people are awaiting rescue, trapped in their homes or seeking emergency shelter.
Rain, some of it heavy, will be possible through Thursday evening for south Alabama.
The president later appeared at a meeting with Gov. Abbott and local officials.
With Harvey expected to make landfall Wednesday in the Bayou State's Cameron Parish, the region may see a Hurricane Katrina-like impact it witnessed 12 years ago. He said the way people got through the storm and that so many lives were saved is "remarkable".
"We know we're not out of the woods", he told KKTX-AM in Corpus Christi.
"It should not be lost that these are true heroes, going into harm's way at a time where government and emergency management is telling people to get out of that area", he said.
Overall damage from the storm is expected to be in the tens of billions of dollars.
Unsafe rescues went on through the night as police, firefighters and National Guard troops in helicopters, boats and trucks pulled stranded residents from flooded homes.
"We want to do it better than ever before", he said. "Not by a long shot".