A rising chorus of criticism emerged from the closed-door Iran briefings at the Capitol on Wednesday, as lawmakers skeptical of the nuclear agreement demanded a reckoning from administration officials about so-called “secret deals” between Tehran and the agency tasked with inspecting nuclear facilities.

Opponents of the deal have fixed on a set of documents exchanged between the International Atomic Energy Agency and Iran, of which the United States is not in possession. But while the administration says such accords are standard practice, critics of the agreement to check Iran’s nuclear ambitions are calling it shady.

“There are two secret side deals, deals that are between the country of Iran and the IAEA,” Rep. Mike Pompeo (R-Kan.) said after emerging from a private session with Secretary of State John Kerry, Energy Secretary Ernest Moniz and Treasury Secretary Jacob J. Lew where House members were briefed on the Iran negotiations. “I just find that completely unacceptable. I don’t see how a member of Congress can vote for an agreement not knowing what the full scope of the agreement actually is.”

Pompeo and Sen. Tom Cotton (R-Ark.) sparked the wave of consternation about the deals on Tuesday, when they released a statement saying the IAEA had told them during a meeting in Vienna last week that they had private arrangements with Iran on inspections of Iranian military facilities and interests that could be tied to Iran’s nuclear program.

“I don’t think that we should move forward with a vote until we have those documents,” Cotton said Wednesday. “I think it’s incumbent upon the administration to obtain them and provide them.”

Administration officials have tried to downplay concerns over the issue by explaining that such arrangements are nothing out of the ordinary.

“Congress has what we have,” said State Department spokesman Rear Adm. John Kirby. “These kinds of technical arrangements with the IAEA are a matter of standard practice, that they’re not release publicly or to other states. But our experts are familiar and comfortable with the contents.”

Some congressional Democrats backed the administration’s argument.

“The IAEA literally negotiates with every country that has either civilian or military nuclear capacity in terms of the inspections regime,” Senate Minority Whip Richard J. Durbin (D-Ill.) said. “That is being done now with Iran.”

Under the terms of the deal, the IAEA is responsible for carrying out inspections of nuclear and suspected nuclear sites in Iran and for, at least initially, attempting to work out arrangements to facilitate inspections when there is a disagreement with Iran about access to a suspected facility.

But the accusation of obfuscation struck a nerve in Congress where many are already wary of the Iran deal’s inspections regime and how much access it will give to inspectors to review and investigate Iran’s enrichment activities freely — especially when it comes to Iran’s military installations, which are the subject of the “deals” critical lawmakers charge are being kept from the Congress.

“I think that when you have side deals it means you’re sort of yielding control over what you’re actually asking for in certain respects,” said Rep. Thomas J. Rooney (R-Fla.). “We don’t have total control or what’s going to transpire.”

And it seems no accident that the latest accusation has held particular sway with the deal’s most outspoken opponents, who have charged that President Obama and Kerry are pushing a bad deal on Congress.

“There was no direct answer to a very direct question: Is there a deal between the IAEA and the Iranians about limiting inspections to military facilities that we don’t know about and the American people never hear about? We never got an answer on that,” said Sen. Lindsey Graham (R-S.C.), adding he believes the IAEA will let Iran take the Parchin military complex “off the table in terms of any real scrutiny.”

“I hope a no vote will be seen as empowering the next president” to get a better deal, Graham continued. “If it is Hillary Clinton, she could do better than this.”

Correction: An earlier version of this story incorrectly identified the state represented by Rep. Thomas J. Rooney. He is from Florida, not Pennsylvania.