Brown said 90% of the city's 50,000 residents were without power for more than two days.
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Galvestonians were also told to boil their water or stop using it entirely when pipes burst from the cold. Brown said water should be restored Thursday.
"Our greatest need right now is we need to get our power up. We need to turn water off to all these homes where the pipes have burst and draining the system and working with the citizens on that. We have a food and a water concern here on the island. We're bringing water in today. The human suffering, though, that is occurring through this is very, very concerning," he said.
He did not immediately put the blame for the crisis on Texas's unique independent electrical system, but he said he did request an investigation from Gov, Greg Abbott's administration.
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Fortunately, the city's hospitals remained up and running throughout the storms.
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"We ran dangerously low of water, but now we're back up. We filled the tanks up, and we're doing fine at the hospital," he said.
Brown said the coastal city is accustomed to recovery, as it's often the target for major hurricanes, but he called the winter storms "worse."
"In a hurricane, you can go to the mainland and get away from this. In this particular situation, no matter where you go in Texas, you still have a concern that is similar to what we have here," he said.
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