Nearly two million people were still without power in Texas, the oil and gas capital of the United States, with some facing water shortages as a deadly winter cold spell that hit the southeastern part of the country headed east.

The National Weather Service (NWS) issued a winter storm warning for a swathe of the country ranging from east Texas to the East Coast state of Maryland.

The NWS said the storm would bring ice, sleet and heavy snow to parts of Texas, Louisiana, Arkansas and Mississippi as it tracks to the northeast, causing power outages, tree damage and making driving hazardous.

Even though the Arctic air mass was beginning to lose its grip on an area of the country not used to such extreme cold, the frigid temperatures would continue, the NWS said.

"The Arctic air will also continue over the Plains and Mississippi Valley with temperatures of 25 to 40 degrees below average," the NWS has reported.

President Joe Biden was forced to postpone until tomorrow a visit to the Pfizer Covid-19 vaccine manufacturing site in Kalamazoo, Michigan, while federal government offices in Washington were to be closed today.

More than 30 storm-related deaths have been reported by media in the United States since the cold weather arrived last week, many in road crashes.

Hundreds of thousands of residents of the Texas metropolis of Houston were suffering from both power outages and a loss of water pressure.

"Water pressure is very low," Houston Mayor Sylvester Turner tweeted. "Please do not run water to keep pipes from bursting."

Nearly seven million Texans were being advised to boil their water before drinking it or using it for cooking.

David Hernandez, 38, spent the night at a Houston church with other people who have fled their homes.

"My car got stranded and I was trying to sleep in the car but it was just too cold," he said. "Liquids in my car were actually turning to ice so it was like sleeping in an ice box.

"I had to come here," he said. "There's no choice."

Power companies in Texas have implemented rolling blackouts to avoid grids being overloaded as residents crank up the heat.

According to PowerOutage.US, about 1.8 million customers were still without power by yesterday in Texas, the only one of the US's 48 continental states to have its own independent power grid.

Karla Perez and Esperanza Gonzalez try to stay warm during a power outage in Houston

Beto O'Rourke, a former Democratic presidential candidate from Texas, told MSNBC television the situation in the Lone Star State was "worse than you are hearing."

"Folks have gone days now without electricity. They're suffering," he said.

"So much of this was avoidable," Mr O'Rourke added. 

"The energy capital of North America cannot provide the energy needed to warm and power people's homes in this great state. We are nearing a failed state in Texas."

Austin Energy, the local power company in the capital city of 950,000, said tens of thousands of area customers were without electricity, but that they were able to start restoring power in some spots, but it was not expected to stay on indefinitely.

The energy company published the locations of "warming centres" set up in local schools.

While electricity companies struggle to get power restored, Austin-Bergstrom International Airport resumed flights after a two-day hiatus caused by heavy snowfall.

Jeff Zients, the White House Coronavirus Response Coordinator, said the cold weather was impacting delivery and distribution of Covid-19 vaccines.

"There's certain parts of the country, Texas being one of them, where vaccination sites are understandably closed," Mr Zients said. 

"What we're encouraging governors and other partners to do is to extend hours once they're able to reopen."

Many weather-related deaths so far have resulted from traffic accidents, but Houston police said a woman and a girl died from carbon monoxide poisoning after sitting in a car in a garage with the engine running to keep warm.

And emergency medical authorities around the state said dozens of others have been treated for suspected carbon monoxide poisoning, while 77 were treated for hypothermia in northern Texas on Tuesday.

A man in Louisiana died when he hit his head after slipping on ice, and a 10-year-old Tennessee boy died after he and his six-year-old sister fell through the ice into a pond on Sunday.

A dozen animals - including one 58-year-old female chimpanzee - died during the freeze at rescue sanctuary Primarily Primates near San Antonio, the organisation said on its website.

The winter storm spawned at least four tornadoes, according to Atlanta-based weather.com, including one in North Carolina on Monday that killed at least three people and injured ten.

Across the southern border, Mexican officials said six people died after temperatures plunged.