The US government issued emergency legislation on Sunday after the largest fuel pipeline in the US was hit by a ransomware cyber-attack.
The Colonial Pipeline carries 2.5 million barrels a day - 45% of the East Coast's supply of diesel, petrol and jet fuel.
The operator took itself offline on Friday after the cyber-attack and work to restore service is continuing.
The US government has relaxed rules on fuel being transported by road.
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It means drivers in 18 states can work extra or more flexible hours when transporting refined petroleum products.
US fuel prices at the pump were largely unaffected on Monday, but there are fears that could change if the shutdown is prolonged.
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Independent oil market analyst Gaurav Sharma told the BBC a lot of fuel was now stranded at refineries in Texas.
"Unless they sort it out by Tuesday, they're in big trouble," said Mr Sharma. "The first areas to be hit would be Atlanta and Tennessee, then the domino effect goes up to New York."
He said oil futures traders were now "scrambling" to meet demand, at a time when US inventories are declining, and demand - especially for fuel for cars - is on the rise as consumers return to the roads and the economy recovers.The temporary waiver issued by the Department of Transportation enables oil products to be shipped in tankers up to New York, but this would not be anywhere near enough to match the pipeline's capacity, Mr Sharma warned.
Sources said the ransomware attack was likely to have been caused by a cyber-criminal gang called DarkSide, who infiltrated Colonial's network and locked the data on some computers and servers, demanding a ransom on Friday.
The gang tried to take almost 100 gigabytes of data hostage, threatening to leak it onto the internet, but the FBI and other government agencies worked with private companies to respond. The cloud computing system the hackers used to collect the stolen data was taken offline on Saturday, Reuters reported.
Colonial's data did not appear to have been transferred from that system anywhere else, potentially limiting the hackers' leverage to extort or further embarrass the company, the news agency said.
On Sunday, Colonial said that although its four main pipelines remain offline, some smaller lines between terminals and delivery points were now operational.
"Quickly after learning of the attack, Colonial proactively took certain systems offline to contain the threat. These actions temporarily halted all pipeline operations and affected some of our IT systems, which we are actively in the process of restoring," the firm said.
It added it would bring its full system back online "only when we believe it is safe to do so, and in full compliance with the approval of all federal regulations".The incident highlights the risk ransomware can pose to critical national industrial infrastructure, not just businesses.
In addition to a notice on their computer screens, victims of a DarkSide attack receive an information pack informing them that their computers and servers are encrypted.
The gang lists all the types of data it has stolen, and sends victims the URL of a "personal leak page" where the data is already loaded, waiting to be automatically published, should the company or organisation not pay before the deadline is up.
DarkSide also tells victims it will provide proof of the data it has obtained, and is prepared to delete all of it from the victim's network.
According to Digital Shadows, a London-based cyber-security firm, DarkSide operates like a business.
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