"Why would you try to keep natural gas prices down to favor other industries?" Pickens asked. "It doesn't make sense. When you export that natural gas, you're going to create a lot of jobs.
"Go ahead and move it out and sell it," he said. "I'd go ahead and let the gas go into the global market."
(See More: Obama: US to Become Net Exporter of Gas In 2020)
When asked about the response of U.S. companies, such as the private firm Koch Industries, to the prospect of rising natural gas prices, Pickens said they had already benefited from cheap natural gas.
"That's fine—that's America, and that's the way it should be," he said. "But they should allow the producers to export if they want to export."
Pickens pointed out that the U.S. enjoys the lowest energy prices in the world, with oil, gasoline and natural gas selling at steep discounts compared with global prices. "Take advantage of it, use it, rebuild the economy on it and go forward."
(Related: Most Resource-Rich Countries Mismanage Natural Resources)
He dismissed environmental concerns over hydraulic fracking, adding that they are a recent phenomenon.
"Nobody ever said anything until recently," Pickens said. "We have fracked over 800,000 wells in Oklahoma and Texas, and nobody has ever complained about it. This is something that has been proven over and over again that this is safe. So proceed and get the natural gas out of the ground and use it."
Pickens said that approval of the Keystone XL Pipeline project "should be an easy one" with potentially 250 billion barrels of oil in northern Alberta—an amount comparable to Saudi Arabia's reserves. The U.S. would be "absolute fools" not to exploit the opportunity, he added.
(Read More: Keystone XL Expansion Decision Won't Be Made Anytime Soon)
"It's unbelievable," Pickens said. "We have been on the back of cheap energy in the United States. Any country in the world that is using its own resources is doing well. And that's exactly what can happen to the United States if we had a little leadership in Washington to take us down that path."
Pickens estimates that the U.S. has 125 to 130 years of recoverable natural gas reserves.
After the interview, Koch Industries submitted a statement to CNBC.com clarifying the company's stance on natural gas. Philip Ellender, president and chief operating office of Koch Companies Public Sector, said:
"We agree with Mr. Pickens' position on exports—to be clear, we are fully in favor of the freedom to export LNG.
Koch Industries believes free markets are the best means to allocate resources to the most number of people at the lowest cost. We believe that the free market, not government, should dictate how products like LNG are bought and sold.
We differ with Mr. Pickens on proposals that would artificially drive up demand through market-distorting subsidies and mandates."
— By CNBC's Paul Toscano. Follow him on Twitter and get the latest stories from "Squawk on the Street" @ToscanoPaul