"The city of Galveston is not in ruins," Thomas said Thursday. "We will rebuild stronger, smarter than ever before."
Thomas urged residents to stay away at least until next week and acknowledged the delay is frustrating.
"I want you, the citizens, to know that I share your frustration, your anger, your anxiety about your homes and your property," she said. "My commitment is to get you back home as soon as possible."
A city decision to allow companies to send workers in to clean up structures led to confusion after some business owners were allowed entry and others were turned away.
Thomas conceded in an interview with The Galveston County Daily News that owners of some businesses not essential to the recovery had gotten in. But she said that was the result of decisions made by police at checkpoints -- not by city officials.
Thomas also was criticized for insisting earlier this week that only she and City Manager Steve LeBlanc could field questions from reporters. That led to complaints from media and residents that too little information was being provided.
"It was a matter of time and nothing else," Thomas told the newspaper. "There was so much swirling around, so many decisions. We had a lot to do, and there was no other reason."
That policy has been rescinded.
Thomas urged residents to be patient and sounded a note of confidence.
"Because of the overwhelming support from the president of the United States all the way down the chain to employees of this city -- we are recovering faster than I thought we would," the mayor said.