The Obama administration has harshly denounced the letter that a group of Republican senators sent to Iran's supreme leader regarding nuclear negotiations, but Sen. Rand Paul, R-Kentucky, insists the letter should actually help the administration's attempts to negotiate.

"I want the president to negotiate from a position of strength, which means that he needs to be telling them in Iran, 'I've got Congress to deal with,'" Paul said Sunday at the South by Southwest (SXSW) Festival in Austin, Texas.

The letter, signed by 47 GOP senators including Paul, warned that without congressional approval, any deal between President Obama and Iran's supreme leader, Ayatollah Ali Khamenei, could be easily reversed. "The next president could revoke such an executive agreement with the stroke of a pen," they wrote, "and future Congresses could modify the terms of the agreement at any time."

In an interview Sunday on "Face the Nation," Secretary of State John Kerry told CBS News correspondent Margaret Brennan that the letter contained "false information" and was "directly calculated to interfere" with negotiations that conservatives oppose.

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Paul, a potential 2016 presidential candidate, insisted Sunday, "There's no one in Washington more against war and more for a negotiated deal than I am. But I want the negotiated deal to be a good deal."

He also said he signed the letter out of concern that President Obama "doesn't care or understand the separation of powers."

"I wouldn't have signed the letter had he not altered immigration law on his own, had he not altered the health care law on his own, and had he not taken us to war on his own," Paul said.

At the annual Gridiron Club dinner in Washington, D.C. on Saturday, Mr. Obama used his otherwise lighthearted speech to admonish Republicans. "You don't diminish your office by taking a selfie. You do it by sending a poorly written letter to Iran. Really. That wasn't a joke," he said, according to a pool report of the event.

Khamenei, meanwhile, has called the letter a sign of "the collapse of political ethics and the U.S. system's internal disintegration." Iran's foreign minister Mohammed Javad Zarif called the letter "unprecedented and undiplomatic."

Sen. Tom Cotton, the Republican from Arkansas who spearheaded the letter, said on "Face the Nation" that he had "no regrets at all" for sending it.

"It's a simple fact of our constitution that if Congress does not approve that deal, then it may not last," Cotton stated.