A side agreement between Iran and the International Atomic Energy Agency on Wednesday became the latest dispute between Congress and the Obama administration as lawmakers work their way through the deal limiting Tehran's nuclear ambitions.

The agreement — signed July 14 by IAEA Director General Yukiya Amano and Ali Akbar Salehi, head of the Atomic Energy Organization of Iran — was announced publicly, but parts of it are secret. And lawmakers are accusing the Obama administration of illegally withholding those documents.

"Even under the woefully inadequate Iran Nuclear Agreement Review Act, the Obama administration is required to provide the U.S. Congress with all nuclear agreement documents, including all 'annexes, appendices, codicils, side agreements, implementing materials, documents, and guidance, technical or other understandings and any related agreements, whether entered into or implemented prior to the agreement or to be entered into or implemented in the future,' " Sen. Tom Cotton, R-Ark., and Rep. Mike Pompeo, R-Kan., said in a joint statement.

Senate Foreign Relations Chairman Bob Corker, R-Tenn., told reporters Tuesday that he and Ranking Member Ben Cardin, D-Md., had written Secretary of State John Kerry seeking documents related to the side agreement with the IAEA, and had met with Energy Secretary Ernest Moniz to discuss them.

"We sent a letter today, both of us, asking the administration for the documents," Corker said.

Corker did not specify what was missing, but did note 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.

The 159-page deal reached in Vienna on July 14 and approved Monday by the U.N. Security Council requires Iran to resolve with the IAEA by Oct. 15 all outstanding issues related to its past nuclear work as a condition of the sanctions relief laid out in the agreement. The roadmap for that process is laid out in the side agreement signed on the same day by Amano and Salehi.

Nonpartisan nuclear experts have noted that Iran's full accounting of any past nuclear weapons work is essential to establishing a baseline for international inspectors to verify the agreement, in which Iran swears off any intent to build a nuclear bomb and agrees to put most of its nuclear program on ice for 10 years in exchange for relief from sanctions that have crippled its economy.

The Institute for Science and International Security, one of the groups that has closely monitored the negotiations with Iran, warned in an analysis released Tuesday that the deal may contain a loophole in which Iran gets sanctions relief without the issue of past work being resolved, and recommended that the United States and its allies clarify that point.

"The [agreement] does not state explicitly the consequences for Iran not addressing all of the IAEA's ... concerns," the analysis said.

Administration officials sent the nuclear agreement to Congress on Sunday, triggering a 60-day period for lawmakers to review the deal, during which President Obama cannot waive any sanctions enacted by Congress. Lawmakers can then vote to approve or disapprove of the agreement, or allow it to take effect without action.

"They'll have access to everything that we have access to," State Department spokesman John Kirby said on MSNBC, insisting that Congress has received "every relevant document in this deal."

He referred further questions on the side deal to the IAEA.

Kerry, Moniz and Treasury Secretary Jack Lew will give lawmakers a classified briefing about the agreement on Wednesday ahead of a public hearing Thursday before Corker's panel.