After classified briefings Wednesday with Secretary of State John Kerry and other administration officials, lawmakers say they aren't satisfied with the explanation of side deals on Iran's nuclear program that weren't sent to Congress, and still want to see the original documents.

Rep. Mike Pompeo said Kerry told lawmakers that he has not read the side deals, never possessed a copy of them, and approved the nuclear agreement without knowing their details.

"These side deals were essential to getting a deal signed in the first place. Iran believed these side deals to be important to an overall agreement, and so should the United States. It is essential for Secretary Kerry to know what's in the deal, and it is essential for the U.S. Congress to know what's in this deal," the Kansas Republican said.

The agreement — signed July 14 by International Atomic Energy Agency 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 there may also be secret annexes as well. Lawmakers are accusing the Obama administration of illegally withholding those documents.

Earlier Wednesday, State Department spokesman John Kirby told reporters the administration was not withholding anything.

"Congress has what we have, and what's being asked for here are IAEA documents or material that is not in our possession. There's no side deals; 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 of standard practice, that they're not released publicly or to other states."

Lawmakers who were seeking access to any agreements between Iran and the IAEA say they consider them essential as they evaluate the larger agreement reached in Vienna on July 14. Obama says the deal will prevent Iran from building a nuclear bomb, and will require Iran to put most of its nuclear program on ice for 10 years in exchange for relief from international sanctions that have crippled its economy.

Administration officials had promised to bring up details of the side agreements in the classified briefings with Kerry, Energy Secretary Ernest Moniz and Treasury Secretary Jack Lew.

"We know their contents and we're satisfied with them," national security adviser Susan Rice told reporters. "We will share contents of those briefings in full and classified session with Congress."

But House Speaker John Boehner and Senate Majority Leader Mitch McConnell insisted in a letter to President Obama that the administration hand over any side agreements between Iran and the IAEA as well, saying that's what's required by a law passed earlier this year giving Congress a chance to review the deal.

The 159-page nuclear deal, 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.

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 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.

Sen. Tom Cotton, who had demanded release of the documents in a joint statement with Pompeo after the two lawmakers said IAEA officials refused to supply them, told reporters after a separate briefing for senators that the 60-day clock should be reset from the point when the administration hands them over.

The best way to stop the clock, however, is for Congress to disapprove of the overall deal, the Arkansas Republican said. Both he and Pompeo also signed the letter from Boehner and McConnell.

Nicole Duran contributed to this story.