With millions of utility customers in East Texas cut off from electricity by the storm, the utility serving the overwhelming majority of those customers said it was working to set up mobile power sources for critical facilities.

The utility, CenterPoint Energy, which supplies power in and around Houston, said that some 2.26 million customers had lost their electric service at the peak on Monday, and that the figure had since fallen only slightly.

The company said it was looking into using mobile generation units to provide temporary power to places like cooling centers, health care facilities, police and fire stations, senior centers and educational centers.

“We are mobilizing all of our available resources, as well as mutual assistance resources from other utility companies, to begin the process of quickly and safely restoring power to our customers,” Lynnae Wilson, senior vice president for electric business at CenterPoint, said in a statement. “We understand how difficult it is to be without power for any amount of time, especially in the heat.”

The utility said it had begun assessing damage to its facilities and rerouting power to transmission lines that had not been damaged.

Once it has assessed the damage, CenterPoint said, it will publish estimates for how soon service can be substantially restored. Customers in the hardest-hit areas should prepare for an extended period without electricity, the company said.

“This will be a multiday restoration effort,” said Thomas Gleeson, the chairman of the state’s Public Utility Commission, discussing the widespread power outages. “It’s going to take a few days to get this restored.”