More than 400,000 were without power on Saturday morning and 200,000 without water, officials said.
Governor John Bel Edwards says the devastation and damage stretch all the way to northern parts of Louisiana.
At least 14 people were killed by the storm - 10 in Louisiana, four in Texas.
In Haiti, which was earlier badly hit by storms Marco and Laura, more than 31 people are now reported to have died.
President Donald Trump visited affected areas in Louisiana and Texas on Saturday.
"One thing I know about this state, it rebuilds fast," he told a gathering in Louisiana.
Mr Trump said the loss of life was a "tremendous number", but added that it "could have been a lot worse".