Sen. Bob Corker, a Republican from Tennessee and chairman of the Senate Foreign Relations Committee, questions witnesses on March 11. (Andrew Harrer/Bloomberg News)

This story has been updated.

The vast majority of Republican senators signed the explosive letter to Iranian leaders drafted by Sen. Tom Cotton (R-Ark.) and released publicly earlier this week.

But one notable non-signer was Sen. Bob Corker (R-Tenn.), chairman of the Senate Foreign Relations Committee and lead sponsor of a bill that would bring any Iran deal before Congress for review. After the Cotton letter was released, Corker declined to criticize the letter, calling it part of congressional "frustrations ... around the Iran issue," but also declined to endorse it.

[Some Republican senators surprised by backlash to Iran letter]

Now Corker has written a letter of his own — addressed to President Obama — taking note of recent speculation that the Obama administration might take a nuclear deal negotiated with Iran to the United Nations Security Council while also taking the position that it does not require congressional ratification.

"Enabling the United Nations to consider an agreement or portions of it, while simultaneously threatening to veto legislation that would enable Congress to do the same, is a direct affront to the American people and seeks to undermine Congress’s appropriate role," Corker wrote. "Please advise us as to whether you are considering going to the United Nations Security Council without coming to Congress first."

Corker's letter comes amid an arcane but critical discussion of just what sort of agreement that the multinational negotiators in Switzerland are trying to reach. Secretary of State John F. Kerry said at a Senate hearing Wednesday that the agreement would be not legally "binding" and thus not subject to congressional review.

As president, Obama has a good deal of ability to ease the unilateral sanctions against Iran as a part of a nonbinding deal. But the U.N. Security Council has also imposed sanctions against Iran, and an element of any nuclear deal is likely to involve at least a partial lifting of those sanctions — requiring U.N. action. (Note that the four non-U.S. members of the Security Council — Britain, France, Russia and China, plus Germany — are also at the negotiating table in Switzerland.)

On Friday, State Department spokeswoman Jen Psaki said Friday that a United Nations role in an Iran deal "shouldn't come as any surprise ... given who the members are who are negotiating this." An "endorsement" vote would be taken by the Security Council fairly quickly should a final deal be reached, Psaki said, but action to permanently lift the sanctions would come later, after Iran had met certain preconditions in the deal's framework.

[Is Obama’s Iran overture like Nixon’s opening to China?]

Hence Corker's vexation at the possibility that the U.N. Security Council might have some approval role in the deal but not the U.S. Senate, which holds a constitutional role in foreign relations.

And if the comparatively mild-mannered Corker is upset at that possibility, imagine how his more hard-line (and, in some cases, politically ambitious) colleagues feel.

Among those weighing in on the U.N. speculation Thursday was Sen. Ted Cruz (R-Tex.), a potential 2016 presidential candidate, who reacted sharply.

"The United Nations has no authority whatsoever to bind the Unites States of America," he said. "If President Obama attempts to end-run the Constitution by enlisting the United Nations to enforce an Iran deal that sets the stage for Iran to acquire nuclear weapons, it would be both profoundly dangerous to the national security of the United States and our allies and also patently unconstitutional."