The hackers known as Darkside said their goal had been "to make money and not creating problems for society".
The US issued emergency legislation on Sunday after Colonial Pipeline was hit by a ransomware cyber-attack. The pipeline carries 2.5 million barrels a day - 45 percent of the East Coast's supply of diesel, petrol and jet fuel.
The operator took itself offline on Friday after the cyber-attack. Work to restore service is continuing.
The hack on Colonial Pipeline is being seen as one of the most significant attacks on critical national infrastructure in history. The pipeline transports nearly half of the east coast's fuel supplies and prices at pumps are expected to rise if the outage is long lasting.
Security expert Jon Niccolls, from CheckPoint said that all the devices used to run a modern pipeline are controlled by computers, rather than being controlled physically by people.
"If they are connected to an organisation's internal network and it gets hit with a cyber-attack, then the pipeline itself is vulnerable to malicious attacks."
Direct attacks on operational technology are rare because these systems are usually better protected. So it's more likely the hackers gained access to Colonial's computer system through the administrative side of the business.
"Some of the biggest attacks we've seen all started with an email,"An employee may have been tricked into downloading some malware, for example. "We've also seen recent examples of hackers getting in using weaknesses or compromise of third-party software."Hackers will use any chance they get to gain a foothold in a network", Niccolls said.
US fuel prices at the pump rose six cents per gallon on the week to $2.967 per gallon for regular unleaded gasoline, the American Automobile Association (AAA) said on Monday, while Wall Street shares in US energy firms were up 1.5 percent.
The AAA said prices were heading towards their highest level since 2014.
However, there are fears that this could change if the shutdown is prolonged.
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.
Demand - especially for fuel for cars - is on the rise as consumers return to the roads and the economy recovers.