Congressional leaders on Thursday stepped up pressure on the Obama administration to provide details of "side agreements" struck between Iran and the International Atomic Energy Agency.

Senate Majority Leader Mitch McConnell, R-Ky., said in a floor speech that Congress has the legal right to review every part of the nuclear agreement between the United States and Iran.

"The law gives Congress the right to review all of the elements of an agreement struck between the White House and Iran, and then take a vote on it," McConnell said. "The law is clear."

He continued, "But the administration has not submitted the side agreements between the International Atomic Energy Agency and Iran to the Senate, withholding the text from both Democrats and Republicans in Congress."

House and Senate lawmakers must vote on the nuclear agreement by the end of a 60-day review period that began Monday.

News of the side deal angered lawmakers and could make it more difficult for the Obama administration to win congressional approval of the deal.

Republican leaders on Wednesday sent a letter to the administration demanding to know what is included in the side deal. In a closed briefing with lawmakers earlier in the day, Secretary of State John Kerry said he didn't know the details.

McConnell called on the Obama administration to immediately provide the details of the deal.

"Congress cannot properly carry out its obligation to the American people until the administration fulfills its legal obligation to the American people, and to Congress," McConnell said.