Texas Governor Greg Abbott held his first briefing on the winter weather crisis three days after millions lost power and access to running water, as a large weekend storm swept through the south-east.
More than 2.6 million residents of the second largest American state were without electricity as of Wednesday afternoon, electricity tracker PowerOutage.US said.
Mr Abbott said 1.2 million Texans had their electricity restored and hundreds of thousands more would soon come back "online".
The freezing weather led to the bursting of pipes not built to withstand such temperatures, leaving many with damaged and flooded homes and a lack of running water.
More than 30 deaths have been linked to the events after the storm that hit the south-east, bringing extremely low temperatures, ice and snow.
Some include deaths caused by carbon monoxide poisoning from attempts to stay warm.
And Texas and the south-eastern region are not yet in the clear.
"Another round of precipitation will be coming across the state in the next 24 hours," Mr Abbot said.
The National Weather Service issued another winter storm warning, saying there may be ice accumulating on Wednesday night into Thursday, adding to the crisis.
Frigid temperatures are forecast to continue for a couple days into the weekend. Mr Abbott said they might rise above freezing some time on Saturday.
It is rare for severe cold weather to hit the southern state. Many of its largest cities have recorded their lowest temperatures in decades.
The wind chill in some instances has knocked temperatures below zero in the northern part of the state.
Homes and buildings are generally not built with insulation to fend off freezing temperatures, leading to increased pressure on electricity systems and to power cuts.
There is growing criticism against grid operator Electric Reliability Council of Texas, or Ercot, which controls 90 per cent of the state's power.
Ercot does not know when full power will be restored across the state, The Dallas Morning News reported.
"We know millions of people are suffering," Bill Magness, Ercot's president and chief executive, said on Wednesday.
"We have no other priority than getting them electricity. No other priority."
The White House said Federal Emergency Management Agency agents were travelling to the state with generators and fuel.
"It has supplied generators to Texas and is preparing to move diesel into the state to ensure the continued availability of backup power which, of course, is a major issue on the ground, to key critical infrastructure including communications, hospitals and water," White House press secretary Jen Psaki said.
President Joe Biden also made an emergency declaration over the situation in Texas this week.
Meanwhile, Mr Abbott is facing backlash over comments he made on Tuesday night.
On Fox News, he falsely blamed clean energy for the power cuts, after telling a local radio station that natural gas was frozen in pipelines.
“Every source of power the state of Texas has access to has been compromised because of temperature or equipment failures," Mr Abbott clarified on Wednesday.
Ercot said all energy sources were suffering because of the historically low temperatures.