White House National Security Adviser Susan Rice said Wednesday that the administration is well aware of an unpublished side deal that Iran negotiated with the International Atomic Energy Agency and is "satisfied" with the result.

She said, however, that the administration does not intend to make the details of that deal public, and instead plans to share the information with members of Congress in a classified setting.

"The IAEA and Iran did reach an understanding," she told reporters during a White House briefing Wednesday. While she said the documents outlining the deal "are not public," the administration has been briefed on the documents and has unofficially signed off on them.

"We know their contents and we're satisfied with them," she said. "We will share contents of those briefings in full and classified session with Congress."

"So there's nothing in that regard that we know that they won't know," she said.

The side agreement between Iran and the IAEA became the latest flashpoint between Congress and the Obama administration as lawmakers begin reviewing the deal to curb Tehran's nuclear program.

The agreement was announced publicly but parts of it are secret. Key lawmakers are now accusing the administration of illegally withholding the documents related to the side deal.

Sen. Bob Corker, a Tennessee Republican who chairs the Senate Foreign Relations Committee, along with ranking member Ben Cardin, D-Md., have written Secretary of State John Kerry seeking the documents and have met with Energy Secretary Ernest Moniz to discuss them.

Other GOP lawmakers, including Sen. Tom Cotton, R-Ark., and Rep. Mike Pompeo, R-Kan., also have spoken out about the side deal, accusing the administration of violating requirements to provide Congress all "the nuclear agreement documents, including all annexes, appendices, codicils, side agreements, implementing materials, documents, guidance and other understandings and any related agreements."

Corker told reporters Wednesday that one of the documents related to the Iranian military facility at Parchin, widely believed to have been the site of past work on nuclear weapons.

At the State Department, spokesman John Kirby echoed Rice's comments and said Congress would quickly be briefed on the deal between Iran and the IAEA.

"There's no side deals," he told reporters. "There's no secret deals between Iran and the IAEA that the P5+1 has not been briefed on in detail."

"These kinds of technical arrangements with the IAEA are a matter standard practice, that they're not released publicly or to other states," he added. "But our experts are familiar and comfortable with the contents, which we would be happy to discuss with Congress in a classified setting."

Earlier Wednesday, Kirby got into a heated exchange with MSNBC's Joe Scarborough over the existence of the side deals.

Charles Hoskinson contributed to this report.