Senate Foreign Relations Committee member John Barrasso said Thursday he's worried about the repercussions of lifting sanctions against Iran.
In a televised speech Thursday, Iran's president said Tehran would agree to a final nuclear accord with the U.S. and five other nations only if all sanctions over its disputed nuclear work were lifted.
"Iran wants the money. They say, 'Show us the money,' because it's tens of billions of dollars when you lift the oil restrictions, when you lift the banking sanctions," the Wyoming Republican, Barrasso, told CNBC's "Squawk Box" in an interview. "It's a lot of money that comes into them, and I think they are going to use it to support terrorism elsewhere."
Last week, both sides in the Iran talks announced that a framework agreement had been reached, with the goal of a final deal by June 30. But a number of issues are in dispute, including the timing of sanction relief, which the U.S. said would be phased out gradually.
Read MoreEx-Israeli PM to US: Give Iran 'or else' ultimatum
"The White House seemed fixated on getting a deal, even a bad deal," said Barrasso. That's why, he said, he's part of a bipartisan group of senators who want the final say, a demand the White House worries would hamstring further negotiations.
The Senate Foreign Relations Committee plans to vote Tuesday on the Iran Nuclear Agreement Review Act, crafted by chairman Bob Corker, Republican from Tennessee, and supported by influential Democrat Chuck Schumer of New York.
President Barack Obama, who's threatened to veto the bill, called Corker on Wednesday in a latest attempt to convince Congress that the framework agreement is the best way to prevent Iran from developing a nuclear weapon.
"I want to actually review the deal. The Senate wants to review the deal" before any Iran sanctions put into place by Congress would be lifted, Barrasso said. "We want 60 days to review the final deal and say, 'Yes or no.' "
"You would think the president would want to come to the Senate," Barrasso added. "It would strengthen his hand. It would give additional validity and credibility to a deal if he had the Senate buying in and approving it."
There's one provision of the Corker bill the president particularly detests, which calls on the administration to certify that Iran has not directly supported or carried out an act of terrorism against the United States or an American anywhere in the world.
The White House is opposed to pegging any deal to U.S. concerns about Iranian support of terrorist groups. Administration officials insist they're only negotiating an agreement to prevent Iran from developing a nuclear weapon.
—The Associated Press and Reuters contributed to this report.