The North Dakota official said on "Fox News Sunday" that offshore oil production should be increased, and that finding new and renewable sources would be beneficial for the nation.

"I believe we need to do a lot of things, including additional production, including offshore production," Dorgan said, "but we also need to move dramatically toward renewable energy, as well."

Meanwhile, Sen. Kay Bailey Hutchison, R-Texas, said on the program that if oil production is eventually allowed domestically, states should benefit from such energy operations.

"It is an incentive that Republicans put in the last piece of legislation, which many Democrats are trying to withdraw, for states to be able to get royalties if they explore and produce off their shores," he said.

When asked on the program if increased oil production in Saudi Arabia would help lower U.S gas prices, American Petroleum Institute President Red Cavaney said any increased drilling should benefit Americans.

"We can't say exactly, but clearly, more volumes of production is going to help put downward pressure on prices globally," he said. "And that's why increasing our access and production here in the U.S. would also help that equation."