Lake Waco's banks are pictured still covered in snow and ice in Waco, Texas, on February 18, 2021. (PHOTO / AFP)

Texas entered a sixth day of freezing cold on Thursday, as the largest energy producing state in the United States grappled with massive refining outages and oil and gas shutdowns that rippled beyond its borders into neighboring Mexico.

Meanwhile, the now former mayor of Colorado City, in West Texas, said he had already turned in his resignation when he wrote a Facebook post saying it was not the local government's responsibility to help those suffering in the cold without power.

The cold snap, which has killed at least 21 people nationwide, is not expected to let up until this weekend

In his typo-ridden post on Tuesday, Tim Boyd wrote: "Only the strong will survive and the weak will parish (perish)." He said he was "sick and tired" of people looking for handouts.

READ MORE: Temperatures to drop as cold air heads south

Boyd deleted his post but stood by the sentiments in a follow-up message. He also wrote that his original message was posted as a private citizen, not as mayor of the city of 4,000, saying "(I) had already turned in my resignation and had not signed up to run for mayor again".

The post was made as millions of Texans had no power following a winter storm. The cold snap, which has killed at least 21 people nationwide, is not expected to let up until this weekend. The deep freeze has shut about one-fifth of the US refining capacity and closed oil and natural gas production across Texas.

Power companies in Texas have implemented rolling blackouts to avoid grids being overloaded as residents try to heat their homes.

The outages in the state also affected power generation in Mexico, with exports of natural gas via pipelines dropping by about 75 percent over the last week, according to preliminary Refinitiv Eikon data.

Texas Governor Greg Abbott directed the state's natural gas providers not to ship outside Texas and asked state regulators to enforce that ban.

Abbott said on Wednesday that "every source of power Texas has, has been compromised", from coal and renewable energy to the state's two nuclear power plants.

Texas accounts for roughly one-quarter of US natural gas production. It exports gas via pipelines to Mexico and on ships that load liquefied natural gas from terminals in Freeport and Corpus Christi. It also supplies numerous regions of the US, including the Midwest and Northeast.

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The ban prompted a response from officials in Mexico, as US gas pipeline exports to Mexico fell to 107 million cubic meters per day on Wednesday, down from an average over the past 30 days of 5.7 billion cubic meters, according to Refinitiv.

About 28.3 million cubic meters of gas can supply 5 million US homes for a day.

The Mexican government called the top US representative in Mexico on Wednesday to press for natural gas supplies.

Power cuts have hit millions in northern Mexico. Major automobile manufacturers halted operations temporarily because they did not have natural gas needed to operate their plants.

Agencies, Minlu Zhang in New York and May Zhou in Houston contributed to this story.